Should see how many times can get through without reusing a character.
First round (ignoring the second of any double-ups for a letter):
Archangel
Beast
Cyclops
Darkstar
Emma Frost
Fantomex
Gambit
Havok
Iceman
Juggernaut
Karma
Leech
Monet
Nocturne
Onslaught
Polaris
Quentin Quire
Rogue
Storm
Tyler Dayspring
Unus
Vargas
Weapon X
X-Man
Yuriko
Zaladane