Thankfully most of this strike can be bypassed and killing very few enemies. No one in my fireteam gets over 20 kills and we usually finish in under 5-6 minutes.
How to Farm Psion Cloaks in Under 5 Minutes on Nightfall
First room: Pull out ghost and clear ads, when the 2nd wave spawns in with the yellow harpy; ONLY kill the yellow harpy. After he is killed everything will despawn and dead people will be auto revived.
Cyclops: Team shoot the first one from the entrance. If done right he won't be able to shoot. Now take the elevator shaft and kill the one on top. Lastly kill the one on the stairs. The cyclops are the only things that need to be killed. The door will open, run through. Dead people will be auto-ressed.
Keep running all the way to pull out your ghost at the door. Then kill the goblins in the gated room, finally kill a yellow minotaur and the door will open.
Lastly, decide who needs what cloak. Then kill the psions accordingly with swords. Tethers and bubbles help with this part a lot. Don't worry about ships/ads just focus on the psions. It's important that you do damage to the psion killed last or you won't get any rewards.
You can see the video below for illustrations on how to do it:
Super simple, you can skip most of this nightfall with very little killing. First part just kill the yellow harpy and everything will despawn, next just kill the 3 cyclops, next skip through and pull out your ghost and then kill the yellow minotaur that spawns.
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Credits: Special thanks to TheRushingFox for the tips and guides.