No way you can catch with 〜っこない
Grammar Explanation: A strong denial with 〜っこない

Asuka Jr. is feeling down after Saint Tail committed a theft without giving him advance notice. When Meimi tries to console him, he tells her she doesn’t understand Saint Tail.
- 芽美 (thinking):
- 「わかるもん…… セイント・テールはあたしだもん!!」
- “I do understand... Because I'm Saint Tail!!”
- 芽美
( : - 「あんたなんか一生
( かかったってセイント・テールをつかまえられっこないっ」- “Someone like you can take a lifetime and there's no way you can catch Saint Tail!”
Key Points
つかまえられっこない is a strong impossibility
つかまえられる is the potential form, meaning can catch.
Adding 〜っこない makes it “there is no way you can catch”, stronger than a plain negative.
一生かかったって raises the stakes
〜たって means even if in casual speech.
Meimi says that even if Asuka Jr. spent his whole life on it, catching Saint Tail would still be impossible.
あんたなんか is dismissive
あんた is a rough casual you, and なんか belittles the person it marks.