Override the mining lander.
Overriding the lander requires you to hold your position nearby until the process is complete. During this time, you'll want to take care of the Cabal's Phalanx and Psion troops early on, ensuring they don't get close. Furthermore, missiles will be incoming from overhead at regular intervals. Be sure to stay out of their blast radius.
Destroy the Thresher gunship.
Once the override has made sufficient progress, a Cabal "Thresher" gunship will fly in from the sky. The craft will circle several times before flying off, meaning you'll want to use a weapon with extended range (such as a rocket launcher) to bring it down while you can.
Defeat the Excavation Valus.
Destroy the three Infiltrator Psions.
The "Injection Rig" mobile base will deploy an orange force field once an Infiltrator Psion is defeated. The rig will also ignite its thrusters at this time, causing those within the force field to take damage. Therefore, it's advised you hang back and wait while the field is up. After it dissipates, concentrate your fire on the remaining Infiltrator Psions that appear.
Destroy all Injection Rig vents.
Since the vents only open while the force field is active, their destruction will require you to take damage while firing on them from inside the field. Further complicating things are the Infiltrator Psions, which only spawn three times in total—giving you but three chances to destroy the vents. Miss any of these, and your hopes of a Heroic trigger will be dashed, so approach the battle with caution. Furthermore, with three upper vents, two central, and one down below, it is not prudent to attempt taking them all out on your own. Victory will require you to exercise some slick teamwork with your fellow Fireteam members.
Defeat the Infiltrator Valus.
Terminate all Fallen that spawn in.
Defeating all the Glimmer-extracting Fallen at a site will prep the next site for combat, where the process is then repeated. Successfully defending all three extraction sites results in your victory. Your next destination will always host a Fallen ship and extraction machinery, so keep your senses sharp. The second you spot these objects spawning in, summon your vehicle and rush over.
Destroy the mini-extractors, positioned next to the larger extractors.
These smaller extractors are extremely hardy and will disappear once it's time to move to the next site. It's recommended you take them out as quickly as possible, using a weapon capable of stacking high, instant damage—such as a shotgun.
Complete Glimmer scan.
After destroying the mini-extractors, your Ghost will commence a scan for Glimmer. This will require you to remain in the area until the scan is completed, while also fending off waves of enemies. As the Fallen will attack in bristling droves, you'll want to make liberal use of your Supers.
Destroy the Arsenal Walker.
Defeating the Captain and Vandal that first appear will cause the Fallen ship to deploy an Arsenal Walker. Keeping pressure on its legs will down it temporarily, exposing the Walker's weak point. Concentrate your fire there to win the battle.
Neutralize the force fields over all of the weapon caches.
When the Walker exposes its weak point, it will also drop Arc Charges. As these are required to bring down the weapon cache force fields, you'll want to pick one up whenever possible. Deposit your retrieved charge in a force field generator (positioned adjacent to a cache) in order to disable the field. Repeat this process until all of the fields are gone to spawn a second Arsenal Walker. Note that as destroying the first Walker before all of the fields are down will end the event, you'll want to mind your trigger finger—as well as the Walker's remaining health.
Destroy the second Arsenal Walker.
Once the second Walker has appeared, you will be free to clear both Walkers out in any order you please. Keep in mind though, that taking on two Walkers at once can be an uphill struggle. Therefore, it is wise to concentrate on eliminating the weakened Walker first. Also note that the exposed weapon caches house Scorch Cannons, which are effective Walker-felling weapons.
Destroy the Prime Ether Servitor.
In addition to standard attacks, the Prime Ether Servitor will use a special offensive ability known as "Servitor's Grasp." When targeted, the technique name will show in the bottom left of the screen as you are warped to another location on the map. The warp itself is not damaging, however, it will bog down your progress—something you want to avoid since public events are timed. The Prime Ether Servitor will also deploy an energy shield which is powered by smaller Servitors close by. Be sure to clean out the latter quickly.
Destroy three Transport Servitors.
Continuing your assault on the Prime Ether Servitor will spawn in three smaller Transport Servitors (different to the earlier Servitors which powered the shield). Fail to destroy them in time and they will disappear, so act quickly. They are not particularly durable, so standard attacks should be enough to get the job done.
Destroy the enhanced Prime Ether Servitor.
The Servitor's attack and defense will be mildly improved with few changes to basic attack patterns, save for the addition of its "Servitor's Fall"—which warps the target much farther away. When warped into the air, for example, the subsequent drop is immense, incurring enough fall damage to cause instant death. Watch out for this one... Touching the Fallen ship hovering up above will also kill you on the spot—another hazard to look out for while in free fall.
Defeat the Abyssal Sorcerer.
Two Ritual Witches will appear at the start of the event. Neutralizing their shields will require you to capture two Hex Circles. These luminous rings can be found near the gate. Work with your fellow Guardians to secure them. After defeating the two Ritual Witches, an Abyssal Sorcerer will emerge from the gate on the far side of the stage. Take this one out too.
Destroy the two crystals.
The two crystals are positioned relatively high on either side of the gate. Though they are protected by shields, they can be brought down by staying on top of the Hex Circles after the Ritual Witches have their shields taken down. Destroying the crystals before the Abyssal Sorcerer appears will then trigger the Heroic Objective. Should the Sorcerer appear before you're done with the crystals, though—your chances of triggering the Heroic Objective will evaporate. Take aim with urgency once the crystal shields are down.
Defeat the "Abyssal Champion" Knight when on Titan, or the "Ul-Heru, Envoy of Savathûn" Ogre if on Mars.
The type of boss differs according to location, with Titan featuring a Knight while Mars features an Ogre. Thus, the attack patterns they use will naturally differ too. Both, however, will appear with swarms of Hive, meaning you'll want to keep Supers at the ready for some instant destruction.
Annihilate the Taken.
When the event commences, a massive Blight will appear in mid-air surrounded by smaller Blights on ground level, with the Taken spawning from the latter. Defeating the Taken will cause the corresponding Blight to disappear, with another taking its place elsewhere on the field. Repeating this process to destroy all of the Taken will complete the event. As the dome-like veils surrounding the ground-level Blights are impregnable to fire, it's recommended you first enter a veil before lobbing a grenade to rack up some instant kills should enemies take cover underneath them. Note, however, passing into these domes will trigger the effect known as "Taken Blight," which incurs damage over time. Try not to stay inside them too long.
Destroy the giant Blight.
The airborne Blight is invulnerable to all forms of attack, unless you have the "Blight Receding" buff in effect. To trigger this buff, enter one of the ground-level domes and then leave, thus activating "Blight Receding" for a total of four seconds. Since the buff's lifespan is short, you'll have to repeat this process a few times. One thing to keep in mind—defeating all the Taken before the big Blight is destroyed will end the event, and you will not be able to attempt the Heroic Objective.
Defeat the Blightmaker.
Defeating the big Blight will spawn the Blightmaker. If any smaller Blights are still active at this point, you're not going to be able to effectively land attacks. Enter the domes and destroy their cores before shifting focus to the Blightmaker.
Stop construction of the Spire.
Completion of the Spire requires ten Vexes to integrate with it. Consistently keeping them from physically reaching the structure is your only way to achieve victory. Should a Vex break through your defenses, however, it will need to stay in the Spire's vicinity for a set period—meaning you will still have a brief moment to defeat it before the integration is complete. Stay calm and collected as you fight, keeping an eye on the number of integrations displayed on the left of the screen.
Capture three plates.
A survey of the area will reveal three white glowing lines extending from the Spire, the ends of which are connected to sync plates. Capture all three to trigger the Heroic event. If ten Vexes integrate with the Spire before you can pull this off, the event will end. Securing the plates requires a substantial amount of time, so splitting up your team between plate duty and Vex defense is recommended.
Stop construction of the Spire.
Though this objective is cosmetically identical to the original, you will now have to face powerful foes such as an Integration Mind and Cyclops. Take care not to pour all your resources into gunning these enemies down—and thus forget about defending the Spire in the process...
Defeat the Vex Gate Lord.
Though the objective seems straightforward at first glance, getting the Gate Lord to appear is a multi-step process.
1) Defeat the required amount of Vexes, which spawn in from either side of the map. (The order you defeat them in is up to you.)
2) Next, defeat the Gatekeepers (Keeper of Ages Past/Keeper of Ages Unseen) that appear, one for each side.
3) The defeated Gatekeepers will drop Arc Charges. Place these in the glowing plates nearby.
4) Once the above has been completed on both the right and left sides of the map, the energy catapult which previously faced inward will be reoriented outwards. Use it to travel to an island, situated a distance away.
5) Defeat the Gatekeeper that appears, placing its Arc Charge in the sync plate located in the island center.
6) The island's energy catapult should become usable, allowing you to travel to the center of the map.
7) Defeat the Vex Gate Lord that appears.
Activate the sync plate on the island summit.
After finishing step 5 detailed above, do not travel to the map center, instead moving to the rear of the island. There you will find platforms hovering around the island perimeter, in addition to several diamond-shaped Vex devices. Destroying them causes more platforms to appear, so blow one up whenever you run out of ground to traverse. Note these devices will eventually disappear if you let them, so be swift about scrapping them. Reaching the top will reveal a glowing red plate. Activate it to trigger the Heroic event. Once the Heroic prompt comes up, descend from the summit and board the catapult from step 6 in order to reach the center of the map.
Defeat the Vex Gate Lord.
The general approach is more or less identical to the standard iteration of the event. One notable difference is the Gate Lord will put up a shield. To disable it, you must defeat the Gatekeeper which will spawn in the instant the shield goes up. Then, you must take its Arc Charge and place it in the plate situated directly above the Gate Lord's spawn point. Getting up there is not possible via a normal jump. You will have to use the catapults on either side (which you previously boarded) to get airborne and place the charge. Once the shield is down, open fire on the Gate Lord until victory is yours.
Transmat the fallen Warsat.
To transmat the Warsat, you must remain by it for the required duration as indicated by the counter. As the transmat progresses, Thralls and Knights will spawn around you, requiring you to cooperate with your team to fend them off until the transmat is completed.
Defeat the three Shriekers.
Advancing the transmat will cause Ugul Gar Wizards to appear. Defeating a Wizard will activate a Shrieker, which you will also need to take down. Repeat this process three times to activate the Heroic event.
Defeat Golgoth, Ichor of Xol.
Your objective will change from transmatting to defeating Golgoth. In addition to Power Weapons and Supers, the Valkyries positioned around the map are also effective tools.
Defeat the wanted enemy who escapes from the cryo-pod. (The race of the enemy will differ according to where the event was triggered.)
Wipe out the initial mob of enemies to lure out the wanted foe. Damage him enough and the pod will begin to discharge a freezing gas—accompanied by a damaging area-of-effect field which persists for a short time. Because you aren't required to fight in close proximity to the pod, hang back until the gas disappears. Or, alternatively, jump on top of an object to get clear of the field.
Freeze the wanted enemy.
Destroying a gas vent will expose the cryo-core behind it. Take the core and lob it at the wanted enemy, repeating a total of three times to transition to Heroic. If you defeat the wanted enemy before you can complete this process, the event will end. Watch your foe's health closely.
Complete the transmat.
Freezing the wanted enemy will spawn a transmat field around him. You will then have to hold position until the transmat completes, gunning down the incoming enemy waves. Take care to stay inside the area perimeter while intercepting the hostiles.
Destroy the Concentrated Ether orbs.
Getting the orbs to appear requires you first defeat all three Dredge Chieftains. The Chieftains will be packing Arc, Solar, and Void shields—in that order—so make sure to utilize the appropriate strategy.
Destroy the Concentrated Ether orbs before they can be absorbed into the Servitor wreckage located in the center of the area.
After beating the Arc, Solar, and Void Dredge Chieftains, masses of Concentrated Ether will appear. Don't be deceived by their gaseous appearance—they are tough and will come in swarms. Use a high damage-dealer with a large clip, such as a machine gun, or a weapon with explosive damage like a rocket launcher. Supers also come in handy here.
Defeat the Reanimated Machinist.
Though this boss does not wield any special offensive abilities, the surrounding Scorn will use attacks imbued with a variety of pesky effects. If you're going to be using Heavy Weapons or Supers, be sure to employ precise timing.
Defend the Rift Generator.
Hostiles will come in from three directions, your job being to intercept them before they can reach the generator, since the event will end in failure if its core integrity drops too low due to taking damage. You can, however, pick up Arc Charges from downed Deranged Abominations, and place them in the generator to offset some damage. Whenever you defeat an Abomination, be sure to pick up the Charge it drops.
Defeat the Taken Wizards.
Clearing out the Deranged Abominations will spawn in Blight. Destroying them will in turn cause three Taken Wizards to appear. Defeat the wizards to trigger the Heroic event. Since both the Blight and Taken Wizards will remain on the map only for a limited period of time and you will not be notified of their appearance, be mindful of your surroundings if you don't want to miss them.
Defeat Vakarsik, Grasp of Quria.
Once the event has gone Heroic, you will be transported to the subspace realm inhabited by Vakarsik, Grasp of Quria. At first, he'll be protected by a shield, but defeating a few of the Taken Wizards will shut it down. Use Heavy Weapons to kill the Wizards and once the boss's shield is gone, seize victory with a healthy dose of Supers.
Triggering Heroic events becomes much easier when cooperating with your fellow Guardians.
It's always a good idea to help those around you, whether they be your teammates or not!
*Some of the screenshots shown are from the Japanese version. The game is playable in English.