I am new to PID tuning and really don't know where to begin.  I have read and watched a ton of videos explaining the concept of PIDs, but I don't know how to interpret the obvious and extremely bad flying of my quad into an adjustment.  P up or down, D up or down, is this a low frequency oscillation or a high frequency?  I took a video of my quadcopter flying and a screen shot of the current settings.  I don't have data logging yet (an external logger is in the mail).  But the machine flies so badly I would like to see it smoother before I start trying to record a data log; I can barely get it off the ground and landed it oscillates so badly.  Can someone take a WAG at what I should change first and the increment.

Current Beta Flight PID Settings
BetaFlight Screenshot

Video
Quadcopter Behaving Badly

HobbyKing Hercules 500mm Frame
Sky 4 in 1 30amp ESC BLHeli
CC3D Flight Controller
AX-2810Q-750KV Motors
Propeller 12x6 Carbon Fiber

PID tuning is very subjective and one persons preference may not be another's. In fact, you may have two exact same quads with totally different PIDs required. but in looking at your screenshot in general I can make a couple observations. I would try lowering both P & I on both pitch and roll, with roll 5 or 6 points lower than pitch (maybe start with Pitch at 55 and Roll at 50). Also looks like your D is too low, I go with the 75% rule when starting a tune (ex: if P=55, try D=40 approx.)

Take this all with a grain of salt as all these numbers are based on what I've experienced in tuning a 220-250 sized frame, and I notice that yours is a 500mm, so I'd expect the #s to be slightly higher.........

You've only see basic PIDs on this screen, if you click on "Show all PIDs" button on top-right you will also see the PIDs used for level mode.

What you could do is to disable the level mode and see if the quad hovers nicely, be cautious though - I don't know if you are familiar with flying in acro mode, that can be dangerous on bigger rigs. That would mean that those basic PIDs are OK and you should really take a look into the PIDs used for level modes.

I repeatedly read from other users that betaflight is a pain for larger birds... I don't really know what the problem is but betaflight seems heavily optimized for smaller (i.e. 5") quads.

Few tipps (some already mentioned above)
- try acro (no autolevel modes), makes finding PID related issues much easier
- lower dterm setpoint and dterm transition sliders (makes PID behaviour much smoother)
- when increasing D, only do short hover tests and check motor temperature

If everything fails, you might think about using iNav instead - from what i hear it works much better for large quads.