I ran mastery-arcane build on 1 challenge mode I've done so far and it sucked. Aswell as Arcane spec overall on trash. Yea the boss-damage is insane, good, steady, raid-boss-damage. But Arcane/Fire is useless on trash. I tried dotting up and spread with Fire but it didnt work, Inferno Blast has way too long CD, so does Combustion, you don't have any viable abilities to use on those trash mobs at all, every massive AoE mage ability is weaker than for example Howling Blast.
I tried going Arcane with Nether Tempest, tried to dot up with nether tempest and run Arcane Explosion + Barrage - same crappy results.
So I suggest going Frost is the best choice for Challenge Modes. Once you get that crit cap, go all crazy with haste and win. I'm about to try it out myself at the end of the week as we've only done Silver and I was Arcane so far.