DEATH BY CUBE

Go to stage 31770-1 (World 6 - OLLIE, Stage 1). A large laser orb should be the only enemy that spawns when the stage starts, move out of the way and let it attack your base, then find a spot where you can touch your base without the laser touching you, you will heal the base faster than he can hurt it. Sit there for two minutes then enjoy your achievement.

Here a nice video I found for the achievement. They show 3 solutions and its the last in the video. Just dash underneath him back and forth in time, like every other second hit dash. Really helped me a lot. Big thanks and credit do to Rooster Teeth.

Buy the Shield character and select stage 4-5.

At first you have to fight of a few shooting enemies. Don't worry. It's true that you can't shoot but you can still reflect bullets with your shield to kill them. So just collect the bullets with your shield and kill the bastard.

After you defeated the big shooting enemies a few small cubes should be left attacking your base. Now just keep in mind. You give your base health back by standing right next to it. And when you only have a few little cubes next to it, you can just stand there and won't take any damage. If any cube gets close to you, use dash and change your position.