Welcome to the hardest mission in the game. This mission was already tough on PS2 but the Vita version makes it even worse with the low framerate and sensitive aiming.
It's split into three sections and each have a checkpoint. The hardest is by far the first part where you must take down 40+ of the flyer enemies. The latter two aren't so bad.
The best way to do it is via the analog stick not the touchscreen. Don't hold down fire but rather tap it like burst fire. Never let the gun overheat over 50% and ideally keep it below 25% heat. Your bullets do more damage the less overheated they are.
Apart from using burst fire there isn't much else you can do but memorize the spawn locations so you don't get overwhelmed too much. It's not THAT bad so keep at it and you'll clear it. Once you've done the first checkpoint the rest is way more manageable and if you die in latter sections you won't have to redo it.
Also don't bother using invincibility as it does nothing during this mission.