I see a couple of things. I'm going to come back to that initial plummet right after you took it off the charger, but a couple of other things first.
It looks like for most of the really steep drops in battery you have no signal at all. That will kill a battery because the phone ramps up power to the radio to max and continuously hunts for a signal. If you know you're going to be in a no signal area for an extended time, you might try switching the phone to Airplane mode and then (if you have WiFi) turning WiFi on manually.
It also looks like you're turning WiFI on and off a lot. If you have a reasonably strong WiFi signal, leave it turned on. It uses less power than cellular data (especially when there's no cellular signal at all).
The battery percentages for Android System, OS, and the apps don't look out of place, so I don't think the issue is a run-away program or process chewing up CPU. You do have a lot of Wake cycles, including one long one when there's no signal and no WiFi. That implies to me that you have an app, or multiple apps, trying to do background syncing. That uses up battery even when you have a signal, and probably makes things even worse when there's none. I'd suggest getting the app Wakelock Detector and letting it run. It will show you what is causing all that wake time. Maybe you can turn off or reduce the frequency of certain background data operations.
For general battery prolonging tips, take a look at this post:
http://forums.androidcentral.com/samsung-galaxy-s3/278622-battery-life-tips-myths.html
Now then, that initial drop, in the first few minutes off charger, sure looks like the plummet discussed in the thread I linked previously. And the sudden drop about 1/4 of the way across, where the line first goes red, looks like it too. I don't have AT&T, so I don't remember everything that was discussed in that thread, but I seem to recall there was a way to turn off LTE, which resolved it for some. You might try that, at least temporarily. In any case, read through the plummet thread carefully, and see what you can come up with.
Otherwise, turn off the cellular radio when you have no signal (airplane mode), use WiFi whenever possible, minimize background syncing, and install wakelock detector to see what's going on there. Oh, one other thing: You didn't post the Screen page, but from the graph page it doesn't look like your screen on time is high, but the screen is using quite a bit of battery. You might try turning the brightness down some, if you can still view it comfortably.