You don't need to - and you probably won't be able to complete all missions before finishing the game anyways. The last missions (60+) are pretty, PRETTY hard. You probably already know that after finishing the game you'll be able to do all the things you missed throughout the game. PLUS you'll be able to complete the Crystarium then.
So I'd recommend to first finish the game and then complete the missions.
If I remember correctly, I've done mission 1-30 before finishing the game. The rest was way too hard. ^^" (And I wanted to see the ending sooo~ badly! XD)
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