A good cover-up is so good that the viewer should have no idea that the tattoo they are looking at is concealing another. Doing cover-up tattoos, however, is not an easy task. A cover-up needs to flow with the body, successfully camouflage the old tattoo, and still read like a cohesive image. Typically, that's really difficult to make a stencil for, leaving many artists to go in freehanding for a proper cover-up.
Take a look at the piece above. Color horror artist Paul Acker is the mastermind behind this piece, and thanks to this fun Instagram snapshot, we all get to see the stages of creating this skull creature. Starting with the tattoo that needed to be covered up, Acker then went through and drew completely freehand on his client's skin to render a base design. Once he had a solid layout, Acker simply went all out for the tattoo.
As you can see from the middle panel, there is definitely way more detail added to the final piece than to the initial skin sketch. Luckily for this client, Acker was able to successfully cover the old tattoo through the shading and implied dimensional gap between the skull and tentacles. In fact, by using the dark black in the opposite corner from where the cover-up is, as well as contrasting the black with a bright white highlight, the eye is perpetually drawn away from the groove where the cover-up is, thus camouflaging it even further.