Learn Croatian: Ti njoj nikako nećeš priznati pogrešku. - You absolutely will not admit the mistake to her.

To form the negative future tense, you use the negative helper verb (here, nećeš for "you will not") followed by the infinitive of the main verb (priznati). A great thing to remember is that unlike the positive future tense, where the infinitive sometimes drops its final -i, in the negative future tense the full infinitive is always kept exactly as it is.

Doesn't nikako nećeš create a double negative?

Yes, and that is perfectly correct in Croatian! Unlike English, where a double negative cancels itself out, Croatian requires it. Whenever you use a negative adverb or pronoun like nikako (in no way / absolutely), the verb must also be negative (nećeš). Together, they mean "absolutely will not".

Why do we include ti if nećeš already means "you will not"?

You are right that the verb nećeš already tells us "you" are doing the action, so the pronoun ti isn't strictly necessary for grammar. However, it is used here for emphasis. Adding ti makes the statement stronger, pointing a finger directly at the listener: "You absolutely will not admit it."

Why does the sentence use njoj instead of the shorter word joj for "to her"?