Hanging a shelf using 3 wall-mounting brackets: How to align the drill holes

Do you need more shelves, or do you just need one of the existing shelves to be at a different height?

If it's the latter, it may be easier for you to add some supports underneath one of the existing shelves like this:

The supports should run the depth of the cabinet, and you can attach them with command strips or double-sided tape. Be careful removing them because shelves are often covered with paper that's printed to look like wood.

If you need more shelves, it may be better for you to build a new shelf using the same idea, but have the new shelf resting on one of the existing ones. You'd lose a little bit of space on the lower shelf, but you'd avoid the risk of breaking your rental agreement and/or losing your deposit. You'd also need to be careful not to overload the lower shelf or the whole thing could come down.

Yes, the drill chuck will mar the finish of the shelf. There is a slight chance of damage to the chuck. Plus, choking down on the bit, like that, obscures your view of the hole (the drill and chuck block it) -- making precision harder to accomplish.

The correct way to do this is to use a drill stop.

Drill stops are less likely to slip than tape or zip-ties, and are much better for precise and/or repeated drilling.

If marring the finish is an issue, clamp a piece of 1/8th plywood over the site and adjust the drill stop accordingly.

PS: A piece of wood over the hole is usually a good idea anyway, when drilling finished surfaces. It helps reduce both splintering and the scratching that occurs when flakes of drilled wood or metal whip around the bore site.