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Couple notes as this isn't as difficult as it used to be after the changes made on healing units classification so they don't really fall in the ranged attack unit penalty:
1) 2-3 heavy DPS is the only thing you need here, a combination of 2 archers + 1 vampire hunter for example would be enough to cover your damage department. Pirate can be replaced with whatever as the risk of losing units or leaking through the right side of the map is quite low if a decent melee is used. Your concern should be just the demon mage and the black ones if you lack sustain.
2) For this run I went with 3 healers, you don't really need that much if your burst is high (Bashira for example) and you use skills on your primary healer, or you run Chydis. Ultimately the monsters are slightly stronger but to the penalty-tier stronger level; they still don't do too much damage except for the mage in melee mode.
3) Should you find yourself lacking damage to wipe the mage, a ranger is an alternative to slow it with traps.