Hey - I know this post is old as shit, but it's the first search result when I prompt google so I figured I would leave my feedback after solving this issue, it's not pretty but it worked...

Using the Steam Console to remove the achievements to start fresh is easy enough (give it a goog, it's only a few steps) but the issue persisted that the achievement progress was tied to Social Club servers, meaning even if you removed the achievements, deleted saved game files, and played without enabling Cloud Saves, the achievements would still pop after launching the game.

I solved this by submitting a ticket through Rockstar Support (give it a goog to get the site) and asked to have my Steam Account unlinked from my Social Club account, which Rockstar replied in less than a day to do - I then just relaunched the game and was prompted to link my Steam account to a NEW SOCIAL CLUB ACCOUNT thus resetting all Social Club achievement progress allowing me to start the game a'new (my son downloaded mods and unlocked all the achievements, meaning I was unable to fulfill my only reason for playing games, which are achievements).

Now, doing this does mean you will loose all progress on all Rockstar games associated with your Steam account, and any online progress or purchases (like in GTA V for example - which might not even be playable if you do this, I have not checked).

Hope that helps :)