Although if I remember correctly, her motivations are at least implied. Back when you first meet her you go see a grave of her friend together, right? Her dialogue implies that Alyssa herself was the one who was supposed to be dead and her friend taking her place was caused by a paradox.

If Noel and Serah went on fixing paradoxes, that little discrepancy would also have been fixed. Self-preservation instincts kicked in.