Defeating the Archmage

The Archmage is a hard-beaten enemy that lives in Container Yard. He looks like Master Mygas, but in other colours. If you meet him, you should use this tactic; or run.

You should see that Rei have Resist, and make him use it every turn. Put a Thunder Ring on Peco and a soul gem, then have him defend every turn, and if he gets killed, re-equip him with another soul gem.
Now for the part with Ryu.
Hopefully you have a Shaman Ring or a Spirit Ring, If not,I dont know if this will work.
Turn him into the GOOD kaiser (Infinity+Trance+Radiance and not Infinity+Failure one) Then keep having Rei use resist and Peco defending, while, for 2 turns, you should use Focus, then when you've used it twice,do a Super Combo on the Archmage, get about 5 hits or more and you'll kill him. The first I did it did like 7 or 8 and did about 4000 damage,and the Archmages HP is only 3000...now his auto-super-healing system wont work.

Thanks to Draksor for this info
 

Beat the Berserker

The Berserker lives on Container Yard aslike the Archmage

Use Ryus accession ability with Force,Fire,Defender and have Rei use Weretiger,and have Momo cast barrier (if she has it) on herself so she can withstand FireWhip,and then just use her for support (i recommend giving her meryleeps War Shout ability,raises everyone power) and have her cast might and stuff like that. Again, equip everyone with a soul gem and when they lose it, give them another one. Give Rei a fire ring and the only thing that will kill him is a direct attack (which misses alot) ,and if it does hit him, the spirit stone will crack, but he wont go back to his normal form (unfortunatly,you cant equip another on him). Use Ryus aura berserker,and when he gets low,have Momo give him wisom seeds like every turn (more on that in a bit...).Try and have Momo use command (Influence???) that makes Rei only attack the berserker.
He'll die eventually.
 

Thanks to Draksor for the Berserker tactic