Not so. Grendel gave in to pain and fled when Beowolf wrestled with him and ripped off his arm.
After Heracles defeated the Hydra, he dipped his arrows in its venomous blood, and the intense pain caused by that venom proved useful in many of his other tasks, and was described in detail. It would eventually, of course, claim Heracles himself.
The pain of Nessus the centaur as he was killed by these arrows was described in detail, and when the immortal centaur Chiron was struck by one, the agony it caused him was so great that he gave up his immortality to escape it.
Heracles also strangled the Nemean Lion which, while not specific to pain, generally requires something along those lines to be feasible. Such a strategy will, in any case, certainly be familiar to any Dwarf Fortress fans.
The pain of the cyclops Polyphemus when blinded by Odysseus is also mentioned.
Hmm... while not pain, exactly, the Japanese hero Susanoo slew the eight-headed dragon Orochi by getting it so drunk that it fell asleep, then slicing off all its heads.
In one version of his myth, the Hittite dragon Illuyanka is killed by the same ruse...
The dragon Smok Wawelski was defeated by a cobbler's apprentice, who fed it a lamb stuffed with sulphur. The pain this caused the dragon was so great that it drank itself to death trying to wash the sulphur out of its mouth.