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I won't give up no matter what happens.
Literal
Even-if-たとえ how-ever [of-の] thing [subject-が] exist-ても, don't-give-up.
たとえどんなことがあっても ('no matter what happens') is a strong concessive idiom combining たとえ + どんな ('what kind of') + ことがあっても ('even if there is X'). あきらめません ('will not give up') — polite negative of あきらめる. A steadfast commitment.