Damping is a skill that is unlockable by an Engineer or Infiltrator Shepard as well as Garrus and Tali.
You NEED a target to unlock this achievement. During combat you can cast Damping against an enemy and then wait until it recharges.
Alternatively a quicker way to do this is to cast Damping on the Citadel Rapid Transport terminals. Once you reach the Citadel you'll find orange terminals that let you fast travel around the Citadel but they also count as targets for Damping. Simply save in front of one cast Damping and then reload your save to cut down on the time it takes for your ability to recharge.
When your team mates cast Damping it counts toward the 25.