Throughout the northern area, you will come across power cores that rise up from the ground. These can be armed by going up to and interacting with them, which will make them glow red. One of the enemies you will come across are powersuits and you'll need to lure them to those power cores. Once they're close enough, shoot the core to make them explode and destroy the powersuit.
Do this to five of the powersuits to complete the challenge. Note that this must be done in one sitting, without exiting that current game.
Throughout the zone are power cores that rise up from the ground whenever you get close to them. As you approach them, you can interact with the cores to charge them, causing them to turn red. Shoot them once they're charged to make them explode. Do this to 25 power cores to complete the challenge.
For this challenge, you need to kill a total of five powersuits without overcharging the power cores that come out of the ground when you get close to them. You'll know you overcharge one when its color turns from blue to red.