Checkout missable achievement "Strike" to kill Hedgie in a specific way. However the "Make It Go Round" achievement to simply kill him is non-missable.
Hedgie can be found at the entrance of the "Exhibition" during the mission "The Brave New World." As you enter the boss fight arena you'll find an upgrade station and save point. Upgrading run speed and dodge under the "Character" category are useful for evading his attacks.
To start the boss encounter you need to raise a statue out of the floor using your electric attack
. Stand behind this first one and Hedgie should charge into it, crashing to the floor and exposing a weak spot. Here you can get a few blows/shots in by hitting the orange nodes. Hedgie will do various charge attacks which can be dodged
and ground shock waves which you can jump over
. Keep your distance and heal where needed. You can raise other statues around the arena to stun Hedgie and expose his weak points. When a terminal pops out the ground you can zap it with the Electric Shok. Once zapped another statue will raise out of the ground, use this as cover again to block a charged attack. Hedgie will crash to the ground, where you can hit/shoot another weak point. Rinse and repeat until he's dead.
Note: Occasionally Hedgie will overheat and open up, also exposing his weak points.