I went off to pick up some pretty seashells to give as a present!

Literal

Present [to-become-にする] pretty seashell [obj-を] pick-[to-get-に] went [emph-よ]!

プレゼントにする '(something) to make into a present / for use as a present' is a relative clause modifying 貝がら — the にする here captures 'intended for / to be used as.' ひろいに (the masu-stem + に) + いく is the purpose-of-motion pattern 'go in order to pick.' Two に phrases appear back-to-back (にする inside the clause, then に行く as the purpose marker), a tidy nesting of the particle's roles.