When I select the left side and copy the curves, trying to paste flipped over to the mirrored selection, I got "no selected F - curves to paste into." Until I created one keyframe for the transformed first! But after that little 'bug' (or spider) It always just copied over the curves of one single leg over to the other side. It's still nice to learn that nice Ctrl + Shift + M trick, but for me it didn't work to just copy all four curves at once.
Oh nevermind... "Select > Select Mirror > Extend enable" was the little missing part. Hopefully that will help people that're lost at this point in future :D