This achievement is
Combined Arms worth 25 gs.
For this you need to use a combo of any of your special powers. You Do Not have to register a kill for this achievement. Just a combo to cause a Biotic Explosion or Tech Explosion.
You can even have your teammates use Stasis or Singularity and then use one of your own abilities. This will stack across Multiplayer and Single Player and should be easily picked up no matter what class you used. Just make sure when using your teammates you have them activate there powers first, then hit them with your own. Any power ability you use while another is active will register.
I found these to be easiest to attain with Tech Armor. You can have Liara shoot a Singularity bomb that will catch a few enemies, then run up and detonate the Tech Armor. It will hit all enemies and register each enemy as a combo.
For Soldiers I would recommend using Cryo or Incendiary Rounds. Once the target is on frozen/ on fire, then use Concussion shot. This will register for you.