Uses STBB Instant Conviction at one of your units. Unit loses 90% of its HP. Usually used once per turn.
Uses AoE BB Genocide Ruins on all of your units when HP below 50%. Causes massive damage. Used infrequently. Deal around 2000 damage to Fire Unit.
Uses AoE BB Ground Rock on all of your units. Used often.
Your best strategy is to quickly kill Lugina in once he evolves, since you can't effectively tank Instant Conviction. Bringing along Goddess Axe Michele is the simplest way, as she gives fire damage to all your units. Crit spam teams, such as Mad God Zebra leader, or BB spam teams, such as Felneus leader, can also work. Revives are a must. Lugina does not cause any status ailments.
Magress has an AoE Brave Burst that causes Curse, as well as normal attacks. It's best to take down him first as Curse can be extremely dangerous. Followed by Eze as his AoE Brave Burst deal higher damage than lance (ATK buff when HP < 50%). Leave Lance for the last one as his AoE deal the least damage and Poison's rate is low.