You are taught how to ground pound early on in the game but just to reiterate; you must jump into the air and hold down the melee button to charge it whilst positioning the cursor on to your target.
The power core is a purple/blue sphere surrounded by a gyroscope frame and is pretty much identical to the one from a previous mission that you have to destroy but is a lot smaller.
When you arrive at the first power core, destroy all the enemies around it and then use climb up on top of one of those posts using the ice/snow to the side of it, you will then need to jump off towards the core and ground pound it.
It may take a few tries but you will have as much time as you need to do it.
Please note that this achievement unlocked for me on Easy
although it states Heroic in the description.
Credit to Reabo for the video: