You might have noticed the medals that are sometimes dropped by enemies. Those count for progress to unlock abilities. On the character screen you can select one (at prestige level 10 two) abilities. Select the empty field and you will get to the overview of all abilities (each with four levels). If you have enough medals you can unlock one. Repeat 34 times. There's a total of 44 different abilities, so choose the ones where you get the medals easy enough.
This will take quite some time, because several of those abilities require special medals that randomly drop. You also have to switch between characters, as there are abilities that only some characters can unlock.
This is going to be one of the last achievements you unlock due to the randomness of the drops and the sheer amount of medals needed.
Update: What you can do to make this a bit less tedious is to look at the upgrade screen and write down which enemies you have to encounter. Then when you do see them in a level just farm them. Kill them, hope for a medal drop, then just kill yourself and restart the level. This is especially useful if you encounter a special enemy near the level start. But still you will only get a medal drop every 1 in 3 runs.