In the course of capturing five forgotten beasts over the last six or seven years at Picksling, I have discovered that their pathing is relatively predictable. Most will take 9 ticks to move one tile orthogonally, and thirteen ticks to move one tile diagonally. Some take slightly more or less depending on the circumstances. I have seen it take twelve ticks to move diagonally, and it can seem to take more or less when the beast is determining a new destination and/or task. Speed seems to be uninfluenced by [FLYER].
Beasts seem to chase the nearest legal target (it is unknown what factors influence legality) and will retarget in anywhere between zero and twenty ticks if their current target becomes inaccessible OR if a nearer target becomes accessible). If they kill their target, it seems to take much longer for them to retarget.
Since they are [BUILDINGDESTROYER:2], they will lock on to targets behind destructible doors and hatches. The article on the wiki
describes the conditions that prevent destruction and since those conditions are instantly alterable, beast pathing and targeting conditions can be manipulated to safely control and trap them.
One last quirk: If a beast encounters a destructible object in extremely close proximity, it will postpone its current hunt to destroy it. I discovered this by accident when I left a second hatch open on a beast's path to a cat over another hatch. In previous tests, a hatch itself has not proved to be a strong enough lure to get a beast to stop terrorizing and massacring cavern inhabitants. However, it does seem that standing right next to a destructible object is enough of a distraction to catch their attention on the way to living prey.
Edit: Forgotten beasts will also fight each other if they come in contact. Two who were wandering around in the first cavern layer, which I haven't tapped for trapping yet, got in a fight in the last few months. The beakless swan won.
All of this would also, ostensibly, apply to Titans.