ToME: the Tales of Maj'Eyal

How exactly do I kill this thing without it popping into an incredible number of full health offspring? Massed AoE, certain elemental attacks, what?

Hit it really hard, or hit the offspring with a big AoE. Damaging status effects also work-the offspring will inherit any status effects the parent had, so things like burning can do a lot of damage.

You can also mitigate it by drawing them into a corridor-they can't spawn in non-adjacent squares, I believe. (Or maybe it's a limited range of squares. Either way, it helps.)

Well, fighting them in the middle of the sand cave worked well, as in not at all.

Best bet in the sandworm lair is to get up against a wall (whichever you can reach that cuts off the most approaches) or teleport out of the room they're stuck in, maybe lead them into a room with multiple traps in it. BCOs generally don't do much damage individually, and if you're not completely surrounded you can usually just regen/heal tank your way through murdering 'em. They're annoying, and dangerous if they get you stuck in a collapsing tunnel, but they're generally not that big of a deal. Just kinda' time consuming to kill.

I've run into some extremely dangerous hordes of brittle oozes doing the Farportal, though. I simply couldn't kill them fast enough or survive their concentrated damage. The only real success I ever had against the breed in that area was with an archmage and powerful, lingering AoE spells.

I use guerrilla tactics. Hack away until things look dangerous, then teleport away. Each new ooze splits more slowly than its parent, so if you keep at it, you'll power through eventually.