I can't take credit for this solution, all I did was copy it from Spartan2491's solution on the TrueAchievement website, but it works great so I figured pass it on.
"Very Simple Way.
Once you have the sticky grenades unlocked and your back at the base head to the firing range. Hit the button and someone will throw an alien out onto the firing range. Simply lift the alien with your ability then aim and stick a grenade on them when they are in the air. Once the grenade explodes step back out of the shooting cubicle and your grenades and ability will recharge instantly. Rinse and repeat."