do repeated spells resolve its first instance before doing its second instance ?

Yes, but with no gap between them. A Repeated spell is a single chain item whose instructions execute twice in immediate succession — there is no priority window between the two executions and no chance for your opponent to react in between (FAQ #9005, Rule 820.1.d).

Practically: the first execution runs to completion, then the second runs immediately after, all as part of one resolution. Any triggers created by the first execution wait until the whole spell has finished resolving before they can go on the chain (Rule 158.3). You make separate choices for each execution (e.g., two different targets), but the card is still only "played" once.