To get this achievement, you must use either form of Professor Quirrell (Professor Quirrell or Professor Quirrell (Voldemort)) to defeat the troll during Year 1, Chapter 2 - Out of the Dungeon. If you're playing in co-op, make sure that Quirrell is the one who gets the final hit on the troll.
To get Professor Quirrell (Voldemort), you must go into Year 1, Chapter 6 - Face of the Enemy in Free Play. In the room with the chess board, there is a dark magic object to the left of the board. Destroy this and you'll get the character token which you can purchase in Diagon Alley.
To get Professor Quirrell, you must go to the pendulum room in Hogwarts Castle. When you get to the end of the area (it's a dead end), you'll see the character token sitting there. Obtain it and then purchase the character in Diagon Alley.
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