The Chimera is a 3 headed beast with the heads of a lion, snake, and falcon. The snake head is infused with acid and provides acid resistance. The falcon head is infused with lightning and is more resistant to such attacks. Finally, the lion head is empowered with fire and as such is resistant to it as well.
The Scimitar of Decapitation really helps out here, it instantly cuts off the lion head and effectively removes 1/3 of the Chimera's overall health. It also loses its resistance to fire and most importantly, removes the Chimera's most powerful weapon: its triple breath attack.
To beat the Chimera quickly, first go the store and purchase at least 3 3-Way Shots, 2 Fire Amulets, and 2 Rapid-Fires. Invulnerability is optional. At level 35 and with the Scimitar, the Chimera is a pushover. The lion is the toughest head of the three and without it, the other two heads quickly fall.