Your first encounter with the regenerator? lol don't bother killing it. Blow of it's legs with a TMP, then hurry away and exit from that area. You'll notice the sound of a regenerator breathing after exiting, do the usual method, shoot off it's legs and immediately. go to the freezing room. Once you got the infrared scope, it will be your weapon to kill regenerators.
Another funny, but long method of killing a regenerator is to have ashley at your side and you should have picked special costume 2 from the beginning for this to work, and have activated the ditman glitch to make your life faster. Once a regenerator appears, tell ashley to wait and the regenerator will start slamming her. You'll notice that every time the regenerator slams ashley, it roars, giving you the chance to knife it. After it roars, immediately move back to prevent the regenerator from attacking you. Then rinse and repeat until it dies.
That method is useful in Professional Difficulty, wherein ammo is a necessity to complete the game.