Win the Buttonless MiniGame against a Manticore
The first opportunity you have to fight a Manticore at the end of Chapter 9, as soon as you activate the third snake and ascend the Tower of Delphi for the second time. A man will be atop the tower rambling on about some spilled apples when suddenly he will be attacked by a giant Manticore. After the scene ends you will engage it in combat.

It is the most difficult opponent up to this point of the game, but totally manageable. Once you weaken it enough that a red halo appears, grapple it with and successfully perform the minigame until it is dead.

You will not run into a Manticore again until Chapter 27, The Lantern of Delos, which is also the last time you will see one.

If you are struggling with this fight on Hard difficulty, or would just like a complete walkthrough, please see this post for a detailed text strategy. The video below also contains the entire fight on Hard Difficulty.