The narrator’s internal conflict in “A Tell-tale Heart” is his guilt for murdering the old man. He resolves the conflict by telling the police where the old man’s body is.
“Villains!” I shrieked, “dissemble no more! I admit the deed!—tear up the planks! here, here!—It is the beating of his hideous heart!”
The narrator actually resolves two conflicts by telling the police where the body is. First, he ends the character vs. character conflict because he no longer has to worry about tricking them. Second, he resolves his own internal conflict of madness caused by the guilt of killing the old man. Interestingly, by calling them “villains” he is maintaining his mad delusion. He admits guilt, but not defeat. They (the police and the heart) beat him by being villainous, not clever.