Kid X-Mas is located at the end of Episode 2.
To achieve this trophy you must defeat him in under 5mins without dying. (That also means without resetting checkpoint).
The best way to do this is to set the episode to lowest difficulty and make sure you have a few health and focus upgrades. You can then get through all 3 phases by just spamming Sensen Fury and using a cooldown combo while dodging some of his attacks.