This looks like it was done with an old Model3D module by TheNexusAvenger. Module3D V6.1 (ViewportFrame Implementation).
Before it had ViewportFrame implementation it would basically warp models to a certain size and position it in front of the camera based on your screen ratio so it gave off the effect that you were looking at a 3D but 2 dimensional GUI object– which is why there is clipping on the object as you get closer to your character. This is avoidable using ViewportFrames. There’s many ways and methods you can go about “shaking” the egg. You can manipulate the camera of a ViewportFrame to give off a shake effect.
I would recommend looking through the ROBLOX API for more information on how ViewportFrames work. Now ROBLOX has added in a “WorldObject” instance which actually helps in adding in simple physics to your ViewportFrame worlds, and can benefit you in creating the effect you’re looking for.
Good luck.