The Pyromancy trainer, Cornyx, from Great Swamp can teach you powerful fire spells. First you have to find him and bring him to the firelink shrine.
You can find him at the undead settlement. He is to be found in a cage from which you have to free him. At the undead settlement you will come across a bridge on the other side there are three undead opponents. Be careful, as they throw firebombed at you. From the bridge, you can already see the hanging cage. In it Cornyx is locked.
- Jump from the bridge down to the cliff path.
- Defeat the two enemies that are on the path.
- Then run to the left and then enter into the building.
- Enable the new bonfire.
- Run to the other side out of the building.
- Move right and walk up the stairs.
- Hold on right and go through the roof on the next step.
- Follow the path down the stairs and go left through the short tunnel with the candles.
- Run straight ahead, up the stairs and around the tower until you reach the hanging cage.
When you reach the cage, then a dialog starts. Select while the dialogue option "Request for instruction in Pyromancy". Then he disappears immediately from the cage and will be teleported into the firelink shrine.
Cornyx from Great Swamp is then in the Firelink shrine near the blacksmith. You go from this to the right down the stairs, then directly across from Orbeck of Vinheim there you will find the magic trainer.
Incidentally, Cornyx of the Great Swamp is not only Pyromancy trainer, but also a Pyromancy trainer who can teach you other Fire spells.