Determine the desired distance you wish to raise the cabinet while it is still attached to the wall and note the distance for later reference.
Remove everything from the inside of the bathroom cabinet. Remove all shelves and shelving brackets or pegs. Loosen all the wall attachment screws using the drill, collecting the washers and screws to make sure none of them are lost. Remove the cabinet from the wall and set it on the working surface with the rear of the cabinet facing upwards.
Using the measurement from Step 1, measure down from each of the previously made holes on the back of the cabinet. Make sure that the measured distances are in the same vertical lines to ensure that the holes match up with the holes in the wall. Mark each position using the pencil. Drill a hole in each position, using a drill bit that has a diameter equal to the previously made holes.
Hold the cabinet up against the wall and line up the holes in the cabinet with the holes in the wall. Set the original installation screws in washers and pass them through the holes. Tighten them securely, keeping the washers tight against the wood but not damaging it.