Catalin's Tutor follows the Old Hand pillory, where you free the fencing master Baltzer of Trier. Win his duel and he becomes a Swordmastery teacher, which makes it one of the most useful Bakir activities.
At the Old Hand pillory, pick the option to make the guards step aside and beat them. An onlooker objects when you free Baltzer, so stand by the prisoner. Baltzer then invites you to his camp.
Go to the camp north-west of the pillory, ask Baltzer to teach you and win the duel he offers. After that you can train with him.
Baltzer of Trier once taught Catalin Dragosti how to fence, which is where the quest name comes from.