Get all of your characters to at least level 11 and Alex at level 12. Have Alex use Vigor and his strength will go up about 22 points on average. Have Luna use Cascade Song on Alex and his strength will go up about 15 points. Have Ramus attack always. Have Nash use Thunder Bomb every turn. Have Alex use Sword Dance. With all the power-ups he should now be doing about 250 points of damage to the slime monster. Have Luna heal whenever needed. For good measure have Luna use Cascade song on Ramus for a little extra damage.