To summerize : you want a camera to move like in a fps but you would like to see someone getting eaten
if you parent your camera to any bone (even via an empty) and the camera shakes, it means your bone is shaking. I guess you want the camera to follow the movement of the head of the player … but it will shake too much as a head - in world coordinates - shakes a lot while walking. (Your think the head doesnt shakes lot, because you compare it localy/relatively with the rest of of the body. )
Solution for no shake : parent the empty to the Armature directly (so go object mode) , bring the empty in front of the face, but away enough so the nose doesnt go into the camera from behind
Solution for less shake: parent the empty to the Pelvis bone or a lower Spine bone, so the camera will move a bit when walking
ive tried this before, and indeed, when a camera is parented to a bone (via an empty) the bone constraint seem to be updated 1 frame later each time so it shakes when doing performing fast moves.
solution : add another camera in the mouth of the giant and switch to it when you want in the game. Or, with python, make the empty go somewhere in the mouth of the giant
global solution : use the camera actuator and make it look at the empty you parent on an extra bone (parented to pelvis bone) . Then you will just need to animate the extra bone (or bone constraint) . The Camera is free from any parent and will not shake