My group and I have often thought of challenges that only certain heroes can complete, for example:
Fanatic's Final Dive Challenges:
Final Dive the Chairman into the Operative to win the game.
Final Dive Omnitron into the last device to win.
Maximum Speed Tachyon:
Do 21 damage in a single shot.
Do 63 damage in a turn.
Haka of Hakas:
Do 41 damage in a single shot.
Heal for 40 HP.
Wrest the Mind Challenge:
Do 42 damage in a single turn without taking any damage.
I'm sure there's more craziness you can pull off (omnicannon, raptor bots, and inventory barrage come to mind)...