The condition comes from Achilles in the Trojan War where the gods told him he could not kill all of the Trojans without help but he charged on anyways, which led to his death. The pride inside of him made him charge into battle so he could keep his pride instead of lose his pride, and then his honor.
It's probably best to let the person with Achilles Complex to find out their own way that they will need help with the task at hand. If you insist on helping before they ask, you will miss one thing and another will happen. You will miss them actually asking for help (they just rejected all of their pride), and jumping in before they ask will just anger them. All you can do is wait for their call for help. Then, if you are not a douche, you will help. If you are a douche, then you should kill yourself before the person with Achilles Complex does.
Sam: You will just be shot down. Look around.
Me: I'm doing it anyways.
Sam: You really do have the Achilles Complex. Want my help?
Me: Hell no. If I wanted it, I would have asked.
Sam: Ok. Good luck.