Along with 'commando' type ops like Bruneval, the paras fought in many campaigns including Tunisia, Sicily and early part of the Italian Campaign as well NWE.
6th Airborne fought as leg infantry for months in Normandy, including armour support, and also took part in the Rhine crossings.
There is certainly more to it than Arnhem and Pegasus Bridge, but tbh finding it all listed in one place is going to be tough, but you can reasonably pitch Paras against everyone from DAK and the Italian Army in North Africa to the Japanese (a brigade of 6th AB served in the Far East).