How do I fight flying, fire-breathing Titan Slugs?

Solution 1:

Shields are great against breath attacks, and ranged weapons are great against flying targets, and of course flying won't do them much good if you fight them in 1 z-level high structures. You can minimize losses by making better armor and providing danger room training to your dwarves, I would not recommend facing titans without at least steel armor/weapons and at least proficient level soldiers. You can also use traps to get rid of them (the sort of traps that involve supports and levers, not just building a weapon trap on a tile), though it may require quite a bit of ingenuity and a sacrificial animal (or migrant!) to lure them into the trap. If you're concerned about fires, fight them where the dwarves are strongest - underground.