Something's Going to Die

I hope it's not a neighbors cat or a nice little raccoon family cause that would be a sad story, but something is digging up my beds and if I find it I'm going to kill it.

Two nights in a row my arugula has been dug up, each time I've lost 10-15% of my seedlings.





 I've got a couple ideas:

1. Wire mesh cage around the bed - this is a terrible plan, it makes my life considerably more difficult when it comes time to work the bed, additionally it will be an eye sore in the yard.
2. Motion activated cameras - This sounds more fun.  If I can see what it is then I can possibly consider an appropriate trap (either kill trap or live capture).  At this point I have NO IDEA what it is, I'm not a hunter or animal tracker!  I can't look at print spacing and determine gait, breed and age?!  I (to use a military term) Actionable Intel in order to proceed.

To clarify; I don't want to kill some furry critters, I like critters, but when something screws with my most important hobby the "animal lover" in me tends to diminish a bit, or at least hide for a while.