For these achievements, you'll need to be an engineer class character. To use these: Press RB and highlight the power you want, then press A. You can map it by pressing X, then all you have to do is hit RB to use the power. Only do that if you're working on one at a time.
To make this faster, use the manual cast for every power you have, then use adrenaline rush. You'll get a second use of every power with that. Now everything will recharge, rinse and repeat.
YOU must do these, ally casts don't count.