Hagrid tells us which teachers are contributing protections:
“Well, I don’ s’pose it could hurt ter tell yeh that… let’s see… he borrowed Fluffy from me… then some o’ the teachers did enchantments… Professor Sprout – Professor Flitwick – Professor McGonagall –” he ticked them off on his fingers, “Professor Quirrell – an’ Dumbledore himself did somethin’, o’ course. Hang on, I’ve forgotten someone. Oh yeah, Professor Snape.”
— Chapter 14, Norbert the Norwegian Ridgeback
This makes it a simple process of logical deduction and elimination.
Midway through the chambers, Hermione lists those which they’ve encountered so far (just after they’ve finished the chess game).
“What do you reckon’s next?”
“We’ve had Sprout’s, that was the Devil’s Snare – Flitwick must’ve put charms on the keys – McGonagall transfigured the chessmen to make them alive – that leaves Quirrell’s spell, and Snape’s…”
— Chapter 16, Through the Trapdoor
At the very next obstacle, they encounter the troll. The chamber after this has the logic puzzle involving the potions, so this is clearly Snape’s work.
By a process of elimination, we can deduce that the troll is Quirrell’s doing, or just wait for Quirrell to admit it in the final chamber:
Certainly. I have a special gift with trolls – you must have seen what I did to the one in the chamber back there?
— Chapter 17, The Man with Two Faces
Finally, as you said, Dumbledore provided the mirror of Erised.
So the protections were as follows:
- Fluffy – borrowed from Hagrid
- Devil’s Snare – planted by Sprout
- Flying keys – charmed by Flitwick
- Wizarding chess – transfigured by McGonagall
- Mountain troll – set up by Quirrell
- Logic and potions – cooked up by Snape
- Mirror of Erised – designed by Dumbledore