How do I clean hard water build up on the corners of my shower doors?

Plain old white vinegar. CLR.

Vinegar. Saturate a cloth with vinegar and put it on the hard water build up.

bar keepers friend

Straight vinegar will work well. Soak a cloth in vinegar and place it in the corner and prop a bottle or two to insure it stays adhered to the glass long enough to soak for a hour or so. Then clean well, the vinegar will help to dissolve the hard water deposit but you may still need to scrub with a brush or srubby kitchen srubber.

Toilet bowl cleaner, like lysol toilet bowl cleaner.the ones worth the special spouts

As Janice suggested but paper towels may get into the corners better. Once you have it clean, you can keep it clean with wet & forget shower OR you can use it 2x a week instead of cleaning and it will clean it but takes a while.