There are a total of 5 mutant powers. You will not be able to get this achievement until very late into the game, if not after. Each power has a 4 circles. Depending on the power, there might be 3 or 4 levels. Hold to fill it up once selected. You must upgrade in numerical order. If you were lucky enough to pick up Gambit's Defensive X-Gene, you will get an XP boost to help out.
Note: If you replay levels that give you a choice on your powers again, don't pick the alternate power until you have fully upgraded it. If you switch it, the only way to switch it back is to replay that level again. If you do have it fully upgraded and switch it, don't panic when you see the new power at level 1. The achievement will still unlock as long as one out of each row has been upgraded at some point.