A320 First Officer reported receiving an ECAM for Engine 2 EGT over limit. A go-around was performed and the flight crew ran the QRH and check lists. Priority handling was requested; the affected engine was shut down and a precautionary landing was performed at destination airport.

Narrative

Aircraft X. ZZZ-ZZZ1. During approach to XXL at 8;000 ft.; cleared for the approach with the APPR psb armed (right around ZZZZZ); we received an ECAM for Engine 2 EGT over limit. Looking at the EGT; we had both recognized that it was in the red over 800*C. Captain commanded ECAM actions to which I had began running. It had us reduce engine 2 thrust to idle to reduce EGT which caused no change and required us to shutdown engine 2. The ECAM elected us to select engine 2 master off. Captain increased engine 1 thrust lever to MCT. Systems pages showed; to which we went through each to see what systems were effected; followed by reading the status page. Eng anti ice went on and the APU was started. After ECAM actions were complete a request for priority handling was made to ATC and a hold was requested over ZZZZZ1 at our current altitude of 8;000 ft. by Captain as I went into COM 2 to run the procedures for ENG 2 EGT over limit and ENG 2 shutdown. Getting set up in the hold at ZZZZZ1 at some point our altitude became uncaptured putting us in v/s mode. We had been -250 originally and +250 during the first turn before getting the airplane to capture 8000 ft. on the outbound leg. While I was running the COM Captain called the lead Flight Attendant to give a brief; sent an ACARS message to Dispatch; contacted ZZZ1 ops; took ATC commands and requested emergency vehicles to stand by for landing. The COM instructed for the cross bleed switch to be in the open position if performance permitted. I should have kept this in auto due to high terrain for the possibility of a go-around. After the COM was complete I had taken over ATC communication and requested our approach for the ILS XXL. As we started the approach I told the passengers we would have them on the ground in approximately 5 minutes and to remain seated with seat belts fastened. Upon landing; 'spoilers' 'reverse green' and 'decel' were called. '70 kts.' was called. Upon coming to a stop simultaneously I informed ATC we were stopping on the Runway while Captain set the parking brake and called for 'flight attendant stations'. The firetrucks did an inspection to which nothing abnormal was found. Captain announced 'remain seated remain seated remain seated'. I then asked ATC for taxi instructions back to the Gate. Emergency vehicles followed us to the Gate. Once parked and the jet bridge pulled up we were met by a Firefighter and Maintenance to which a logbook entry was made and phone calls made to both dispatch and a Chief Pilot.