I play this alot. For wizard in the coliseum shoot for the aoe type stuff, chain lightning and meteor. Theres a slow skill you’ll want, ice storm or blizzard maybe, I forget the exact name. Teleport is also a must. Get items with the best cooldown reduction, then keep everything slow and spam your aoes, teleport away when something gets close.
In addition, I would recommend just trying to unlock every skill first and then beat the final boss. After that you get to create whats called a “+ character” which starts you over with access to all the skills so you can customize better.