A friend (ikr hard to come by)
A warlock character
A Deafening Whisper (any energy grenade launcher will do)
Anarchy (any heavy grenade launcher will do)
Time and Patience (or should I say Patience and Time hehe)
Some charges of light (no not the mod, the thing you buy from Petra to active Blind Well)
Step 1. Equip the wares shown above along with top tree dawn
Step 2. Get into a fireteam with your friend
Step 3. Enter the Corrupted Strike
Step 4. Make your way over to the Blind Well and if its not already active, activate it
Step 5. Get a kill with your melee charge to active Sunbracers and go ham with your solar grenades while also utilizing your grenade launchers to rack up as many kills as you can. If you end up completing the Blind Well, input your charge of light in the center to restart the blind well. Do this until you have complete the first part of the quest. (expected time: 1-2 hours)
Step 6. Play Mayhem. Mayhem is a crucible gamemode that comes up on a weekly rotation. Luckily for you, Mayhem is the gamemode this week until Tuesday reset. Use a shutdown super like Blade Barrage or Chaos Reach. Each game should give you 3-4 percent per completion, and trust me Mayhem games are quick. Do this until you complete the second step. (if Mayhem is not the weekly gamemode, just run Gambit or nightfall: the ordeal, although they are not as fast as mayhem, they give you the same amount of progress) Or just wait until Mayhem is live and run it until you finish the second step of the quest which completes the quest itself. (expected time: 1-2 hours)
Step 7. Run back to Banshee and reap your reward
And thats all there is to it. Enjoy.
TL;DR Play blind well in the corrupted strike with a grenade and grenade launcher loadout. Run Mayhem as much as possible or Gambit/Nightfalls.