Be sure to have an open party slot, there is no cryosleep chamber here.

Step One: Get yourself an Undying Rogue dude.

Step Two: Get yourself a Static Assault Shield.

Step Three: Get a Neurolimit R.

Step Four: Get two stinky shoes. Yes, they do stack speed.

Step Five: Equip your Undying dude with all of the above. He is now borderline invincible.
Step Six: Deploy your dude ALONE (he will usually go rogue during the fights).

Step Seven: Beat those drones down with your electric shield.

Step Seven-Two: AVOID THE RAILGUN AND THE CANNON.
It will still kill. Wait for a good opportunity, the top of the arena is a good place to quickly sprint through. Watch how the drone paths in the arena and note the places it gets stuck going between, or keep your dude in the helibase and wait for the drone to come close, then deploy your dude when it's going away.

Also, keep in mind that the drones must be beat every time you return to this mission. It's a great way to get some expensive guns though.