The above solution is very good, and helped me keep track of what was needed.
However it is possible to obtain this achievement as early as level 2 and without spending any Abstergo credits.
I purchased the copycat perk and while I was playing the 8 game modes, I intentionally got myself killed so that I could steal other players loadouts. Once I respawned I would simply hit LB, RB and Y to use all the stolen actions (these do not have to hit, just be used).
It may take a little luck finding all the combinations, but all I was missing and had to buy after the 8 games was animus shield as nobody who killed me had it in their loadout. Once purchased, I went into a game, hit LB and pop.
Hope this method works as easy for you and stops anyone who was considering using micro transactions to afford all the abilities.