You must unlock all skills, these include everything in the following categories: Biotics, Abilities, and MeleeBiotics
I can't recall totals for each category ( I believe Melee and Abilities are 500 credits to purchase and Biotics are 1000 credits each).
You do not need to level anything up, simply buy them to unlock this achievement.
There is also an achievement for leveling all of these abilities to max level which will cost 69,000 credits total:
This will most likely be your last achievement in the game, best thing to do is finish the full game, then grind the last boss or X1 boss, they both give 1,800 credits each.