As a promoted magic user, Balmer might seem like a volatile unit, but he is not that difficult. Have Rhys use Ward on either Ike or Mia to boost their Resistance, then have either swordsman attack Balmer with an Iron Sword (so they don't lose Attack Speed), which should bring him down in a few turns. Use Ward again if you need to replenish Ike or Mia's resistance rating.