1. based on his actions, Achilles seems to be brave by warning Patroclus and helping him so that he would not lose his life. ( Since you did not provide the text for this answer, just search for some parts in the passage that matches this description.)
2. He has been willing to sacrifice his life for his pride. Since Achilles wants to be the hero so much, he puts his life on the line all because of his pride. His pride causes him to act brave and seem fearless but his pride is slowly eating away at him. Because of this, his pride could just be his downfall if it continues.
3. Because of all his pride and wanting to be the hero in everything to save everyone and to be the star, he went against something he could just not beat because of his pride. His pride caused his downfall.