Yeah, spamming magic is the primary thing you need to do for most of the bosses. Some just have more difficult stagger meters. The important thing to remember is that the system still functions like it did in FFXIII and FFXIII-2. Magic increases the stagger greatly while physical maintains the stagger/slows it's decay. So you need magic to hit the stagger, but you need a physical hit once and while just to make sure you're keeping your meter from completely disappearing while you recover.

The final day gets pretty rough with the new monsters introduced.