The allusion refers to Achilles who was a Greek hero in the Trojan war and was killed in the end of the war by an arrow in the heel. The person who killed Achilles was called Paris. This is a literary allusion because it relates to Greek mythology. The weakest part of Achilles body was the heel.
An “Achilles heel” means the weak part of something.
In this example, the allusion means that telling Trinity the plan of making Ashley a surprise party was the Achilles heel because she could spoil it. Also, they are afraid to tell her about the surprise for Ashely as she could tell her about the surprise. In my opinion, it adds interest about Trinity’s character and sends the message that she cannot keep secrets.