So like I have 75 Fragments and what's confusing without spoiling is the two large levels for instances the one with enemies "8/12 Fragments" the other with no enemies "0/11 Fragments"
 
I basically can't figure out how to acquire the Fragments from those levels let alone several other places where it's not made clear at all where how I can get the Fragments
 
I'm also having a harder time getting Wild Artifacts the only one I can clearly get right now is from The Casino

@ShinjiEx: If you tell us what areas they are we could give you a more detailed response.

Like Demos says it would help if you said which ones you need.... but if I recall those numbers and descriptions sound like the Steppes and Academia 4XX. 
 
Assuming that's true for the Steppes seeing as you're missing 4 and there are 4 large monsters I assume it's those. Kill Long Gui and then talk to townsfolk to accept other quests to kill the other enemies.
 
In Academia 4XX 9 are from quizzes, 1 is from filling your entire bestiary and 1 is from a paradox ending involving the graviton cores.