This can be done after you beat the first boss and get the Drone. You'll need a large number of whatever the in-game credit equivalent is called. I think it took me about 15,000 or so. If you don't have enough, go back and play some levels that have lots of fast spawning enemies and wipe them out to earn more.
When you start the next level after the Drone is awarded to you, you'll be given an option to select it (you can't avoid it). Instead of just selecting it, you also get an option to Upgrade it for more firepower. Just upgrade this as many times as it takes to get the progress bar indicator all the way to 100%, and the achievement will pop.