While there are a lot of enemies in the beginning, most of them will stay in place and use buffs on their first turn, and the 2 spellblades will use magic shield buff on their team.
The gunner soldiers often use a 2 hit attack, and can also use ranged explosive damage in an area. Since there's a lot of them, make sure to stack up on missile resist for your tank so they don't get chained to death.
Lightning Units Only
Since Cloud is a pretty strong damage dealer, you can clear the "Only Lightning Element" units mission even if you barely have good Lightning units by using the trial npc Cloud. Though, it may depend on your available VCs. Equip your units with some damage increasing effects like the one above, and bring some missile resistance and recovery items.
If you used up the Cloud trial npc friend unit, you'll have to ask for help from someone with a strong Cloud, or play the quest in multiplayer with a strong party.