Grey matter is an anti shooter, or a shooter without bullets.
Essentially you're the bullet.

Run into the exposed brains of incoming attackers to destroy them.
Killing 3 of the same type of enemy will cause a "Trinity attack" killing everything inside it.

Avoid enemy dangers (flashing bullets, tails, teeth and lazers)

Tips.
-You can upgrade at any time in game by pressing P or Esc to pause the game.
-Shields are most important and should be purchased first.
-Holding shift will not only slow you down for better control, but it will also extend, and speed up your options that spin around you.
-Trinity Attacks will increase your chain multiplier which gives you more points for upgrades