You may feel I sound like one rodent,
though in-principle I do meet its characteristic.
Quirrell rhymes with squirrel. JKR writes, Quirrell which is so nearly "squirrel"-small, cute and harmless-also suggested a "quiver",a nod to the character's innate nervousness.
I set out on a quest to find the strongest coal,
hoping to illuminate and fuel my goal.
Quirrell set out to hunt for Lord Voldemort (strongest coal, used poetically as a storehouse of power) in Albania where he was believed to be hiding, hoping to learn skills(strike the coal and thus absorb its illumination) from him and then come back and carve a niche for himself and be recognised,(i.e. to fuel his ambitions). JKR writes that he had a latent desire to make the world sit up and notice him. And he believed that the Dark Lord would grant him his privileges as he was the one who found find and nurse him.
Success I accomplished so I felt,
but slowly, reality hit me with a pelt.
Upon finding him, he believed himself to be successful but he gradually realised he was grossly mistaken when Voldemort took possession of him and used him as a puppet to instead nurse his own ambitions!
I realised I was crying and drowning,
as the devil inside was rapidly breeding.
Quirrell protested to him, begged him to be freed but Voldemort was too powerful even in his weakened spirit form and went on breeding on him(inside him) more and more.
My services culminated in my brutal end,
a pain so terrible by a foal which master did not apprehend.
Quirrell's whole being was so mutilated and weakened by his slavery services that it finally led to his end when Harry, a foal(term used for the underage by the Centaurs) killed him. The intensity of this protective charm was something Voldemort(master) had not completely foreseen and fled from Quirrell's body just in time to save himself, leaving Quirrell behind to collapse and die.