Destroy slimes with any of the weapons available to you - A turret, minigun, lasers, grenades, even a multi-turret! Some slimes are tougher than others, some even shoot back at you. Blow up enough of them, and you'll eventually level up!
Every slime you kill drops experience orbs - Pick up enough to level up and get an upgrade of your choosing.
The more upgrades you get, the faster you kill slimes > The faster you kill slimes, the more you level up > The more you level up the more upgrades you get. It's a vicious cycle that eventually leads to total mayhem!
just be careful not to die in the process...