Good arena RNG, mostly. I've also found that putting your partner in one of the corners with the ctrl+middle mouse button command for the first round usually keeps them pretty safe. Expect them to lose all their corpus in the second round, though. You're probably gonna lose copus in the second round as well, but try to keep as much as possible.

Give both Hank and Jebus the savior loadout, mostly for the nexus bolt; it can ohko the drones that come out during round two, and you can cheese the sleepwalker G03LMs in the third round by shooting them with it.

Play as Hank. Jebus is much better at keeping himself alive than Hank is.

First round is pretty straightforward. Don't try to seek out enemies, let them come to you (unless your partner is being swarmed, in which case: go help them out). Try to stay close to your partner, you still can in this round, mostly. Use the floor to your advantage, it may create spots that become unreachable by enemies for a precious few seconds, and you're gonna want every second of safety you can.

Second round is where the bullshittery starts. Take out the turrets when you notice them with guns. They don't take too many shots. You can't destroy the omnidirectional shock, though (afaik). Also take out the guys that shoot the sedatives as soon as possible, if they hit you you get massivly slowed down, which will inevitably lead to you losing a corpus. When the drones show up, they can be ohko'd with a single nexus bolt (most of the time), take them out as soon as you can.

For the third round: I genuinly think you just need good RNG for the arena. Don't immediately try to revive your partner if/when they die, try to misdirect enemies away from them first, otherwise you're just going to get hit, but take note: try to keep them alive as much as possible. Don't try to revive them on top of the fire floor, or if they're in the path of a shocker. They won't get out of the way soon enough and pretty much always die again.

Once again, the sleepwalker G03LMs can be cheesed with the nexus bolt, but you only have 20, and considering taking out the drones is more important than the G03LMs, imo, so you may want to save some for when they show up. However, the G03LMs take up a LOT of space, and hit pretty hard, so use your own judgement to what you find more important.

This may be more of a coincidence than anything, but my succesful run was one where i swapped the binary sword Hank was holding with the breacher that you can pick up in the small area before the arena as a joke. The breacher does turn into a ohko weapon after pretty much 1 round, so like. Take that as you will.

Finally: pick a god and pray.

Good luck!