How to Complete Pearls in the Deep
The objective is to defeat the Lord of the Flowsand. The law forbids actions by Nu Mou. This law is easy enough to avoid: just don't use any of your Nu Mou units in this battle.
This can be a very challenging battle. Because of the rough terrain, your units will not be able to move very far each turn. Furthermore, the Lord of the Flowsand (a Yowie) has some very damaging attacks. Gravity Well damages all of your units, and Draw In allows the Yowie to steal HP from one of your units. The Yowie can only use Draw In if one of your units is close to the Yowie, so you can avoid that attack by keeping your distance and using ranged attacks. If you have any units close to the Yowie, it will randomly use Gravity Well or Draw In on each turn. Otherwise, if none of your units are nearby, the Yowie only uses Gravity Well. In other words, you can reduce the chance that the Yowie will use Gravity Well by allowing some of your units to be close enough for the Yowie to use Draw In.
More Antlions will keep arriving on the battlefield if you kill them, so you might want to ignore them.
The Yowie is weak to Wind, so units that know Air Render can be a big help.