How do I Deal with Living Statues and Raiding Tarts?

[Agema]

Living Statues as I recall don't have immunity to the elements, so attack them with troops with high strength or a big weapon, or any spells that deal high damage. All you really need to do is beat their protection (astral has armour negating damage spells).

Tartarians are trickier. You're Rlyeh, so astral is your strong point, water being mostly useless against them.

If it's got astral magic itself, teleport several astral mages in with gems to cast "Magic Duel". Might lose a few of your mages, but worth it. If the tart doesn't have astral and there aren't other astral mages with them, Mind Hunt them with S4 mages and as much penetration as you can supply for each mage casting it. They'll die eventually.

In battle, try Soul Slay with astral, again Pen boosted, with plenty of chaff to soak up the Tarts attention to give time for one to work. Mind blasts will probably paralyse a Tartarian eventually if you can get past its MR. Again, penetration boosts will help your mages.