After beating the game on Veteran difficulty in Single Player you will unlock Master. If you clear Veteran while in co-op it will not unlock. If this happens you can either find someone that has it unlocked already and play with them for one level, or re-clear Veteran for a second time.
In Master every time you destroy an enemy it will shoot back a slow moving, short range attack at you. This coupled with the increased speed and health of enemies makes it a real challenge. Don’t even bother trying to clear the first level with Nemesis because it takes absolutely forever and the boss is even worse.
For those that are skilled with it, Phobos will decimate the first level after it gets the first weapon upgrade. Overdrive is invaluable on Master because there is no retaliation attack and you can clear out literally everything. If you rotate it with your bombs and tap boosting you won’t be touched.
If Phobos doesn’t work out there is always Ferox. It’s an extremely safe ship to play on Master. Its main gun pushes enemies back which keeps them from getting in range for the retaliation to do damage. The boost is also on low enough of a cooldown that you can flee safely and even mix in some overdrive.
Once you get used to the revenge attacks this difficulty isn’t that challenging at all. Just don’t put an emphasis on saving humans because it will get you killed.