biotin Looks like watermarks with tons of dirt around it . Give it a good wash + clay should do the job. Or u could wash + use compound to buff it off ( Meg's ultimate compound works wonders). However, if its clear-coat etching from acid water .. u got to do paint correction   

Saw this video, and I will never achieve such a clean car by myself ( not enough energy  )

120 hours.. 4 hours and i'm already dying from hand-compounding + window cleaning 

biotin couldnt see clearly from your image to know what type of stains u had on your paint..

First we need to know your paint condition.. Then we need to know type of water spots (if that was water spots) that u had..

Type 1 water spots - u can use those water spot remover from the shelf (aeon/ace hardware/etc)

Type 2 water spots - u can use ultimate compound whether by hand or machine.. Use it wisely

Type 3 water spots - etching into clear coat and I'm not sure can be remove. I have one on my car paint..

Honestly for me claying wont remove water spots.. I have so many type 2 and claying wont remove them..

Remember. Using ultimate compound will cut your clear coat.. So if I were u, i will use something less abrasive first to remove the stain (since I dont know which type u had)

Previously I use UC to remove my type 2 ws and after doing some research, how I wish i use Duragloss Water Spots remover first before UC.. More effective and more safer to clear coat..

Choice is yours.. Patient.. Learn and decide.. Im still learning so hope if Im wrong, sifu please correct me ya..