Pilot reported a cylinder failure on take off; resulting in a slow climb rate and sluggish acceleration. Flight crew returned to departure airport and landed.

Narrative

We took off Runway XX. At Takeoff the airspeed was low. Like 76 knots well into the climb when I have a normal pitch attitude. Then I pitched a bit down; still hard to build up airspeed but got to 79 knots. Then I said out loud why is it struggling to climb? He said you forgot flaps. I said no; I'm trying to get the airspeed to retract flaps from 50 to 0. I was pitching down continuously while talking to him. It took a pitch down to pretty much the horizon to get 85 knots. I retracted flaps. I asked if he heard how loud it was getting. He agreed. He looked over and said but we have 97% power. Then looked down and and said cylinder 3 is out; my controls. Cylinder 3 was white (as opposed to green). Then we began to feel vibrations. Person A immediately turned toward the downwind and spoke to ATC (he said he should've said pan pan) but limited time. Then I noticed we weren't climbing above 1;400 feet and even then had a slight 100 FPM descent. Tower cleared out the pattern told everyone to go around and climb to TPA; extend etc. and cleared us for a short approach. When Person A saw we weren't gaining any more altitude he asked tower if Runway XY was available. They cleared us so I did checklist and flaps and he slipped us AGGRESSIVELY towards the Runway. However it was incredibly stable and well done. We landed and could only turn off of Taxiway 1. It wasn't a high speed taxiway so he decided to roll down to Taxiway 2 just in case; he didn't want the engine to die before we were clear of Runway. There were no CAS messages alerting us of any issues with power or engine failures and performance. The information on our display seemed counter intuitive when we were down a cylinder but still indicating full power. We taxied back without incident and called maintenance. A tech came out and did a surface level evaluation of what could've gone wrong and was unable to find anything. I squawked the aircraft and discontinued the check ride.