Mack is the only person who can do melee with your current party, therefore use your casters first turns to beef up Mack's physical abilities (powera, speeda, etc.), and have him use combo until he runs out of MP, and use your casters to cast shield, barrier, regen, and throw flara bombs.
Wait... I could have used Bombs?! Ugh! I thought they count as magic, so I didn't bother.
I had Ming and Cooke cast the buffs and had Mack buff up his attack power. Then I had Mack attacking with a Bio Ring Ultra (with mostly perfect hits), dealing about 900 damage. Had everyone else on support. Ice Magic Beast's attacks started doing 0 damage once I had everyone with Barricade/Shieldus and Covera. Only had to worry about Freeze status.
When you tour outside the U.S., Freezepop says to tell people you're from "near Canada."
Mack is the only one who can do any decent damage in this battle. Use Powerus on him, and have him use Double Hit or whatever skill he has that lets him hit multiple times in one turn. Have the mages spend all their time healing and casting Coverus on the party members. The Coverus spell makes this battle a piece of cake.