Chimeras have been defeated. It’s been done before. Any man worth his salt has heard the story of Bellerophon and his winged horse who basically fought the beast like a coward, flying just out of its reach and raining arrows down on it. I will teach you a much more suitable method for conquering this beast involving nothing more than your hands and a basic knowledge of nautical knot-tying.
Start by getting a good hold on the snake-headed tail of the creature. You’ll need a decent amount of strength to carry this out, but as you’re reading a compendium on monster hunting, it’s assumed you’ve already met that requirement (If you have inadequate strength, may I recommend a job at a dressmaking factory?). Once you have the serpent in your grasp, subdue the beast’s fire-breathing dragon-head by tying a simple anchor hitch (illustrated above for those of you who grew up weak and uneducated).
Tied in such a way the Chimera will have a real challenge doing anything other than just laying there. I recommend butchering the creature as they are a veritable treasure trove of goods. Milk from the goat, leather from the lion, poison from the snake, and the best dragon venison I’ve had in my life (most likely due to it’s proximity to mutton and lion’s meat).