To obtain this achievements you need to complete all the gigs (the yellow esclamation/question marks on your map) AND all the blue ones (related to the police). You can find them easily on your map (if you have trouble finding some of them, there are plenty of videos on youtube, or check Powerpyx site, all credit goes to him and his team).
What I want to UNDERLINE are a few key notions:
1) In some case, while completing the cops quest, (basically the blue-cube icon with a ? ), as soon as you'll grab the loot, the quest will CONTINUE (usually changing name). Most of the times it's just to go to another part of the area to collect additional loot. Sometimes it may lead out of Watson, but what it is IMPORTANT, is that you NEED to complete these "hidden" parts as well. As an example, the quest WORLDY POSSESSION is under this category (but it's not the only one) and you have to complete it! Thanks to Epic Louie and the others who confirmed that.
2) There are few secondary quests (not Gigs, but proper quests) that STARTS in Watson but they do not count for this achievement, such as the fighting pits (Beat on the Brat), the cabs one (Epistrophy), the street races, the cyberpsycho (the one in Watson yes, the others no. To be more precise in Watson you have 5 c-psycho, that have their own little quest, you need to do them, but not the main one, to neutralize all 17. There is another achievement tied to that) and the tarot ones. There may be more, but those are the ones I remember. The ones tied to the achievement are the YELLOW AND BLUE SIGNS on your map. Important NOTE: you need to reach a certain street cred level to unlock all the cops and yellow pointers. For the first area should be around 35 (could be lower though). I did mine while I was around 37, but as I said it was glitched, so could be way lower.
Moreover, you do NOT NEED to buy any car for this achievement to pop. There is another achievement related to them.
3) If you started to do that before patch 1.04 (as I did), it may have happened that you finished some quests, they don't appear anymore on your map, but they are still stuck on the journal and you not have received the rewards, because Regina did not call you. That happened to me with 5 quests (I was stuck at 98% for quite a long time) and the way I was able to fix this (without reloading hours of content/restarting the game) was the following. GO FIND THE CYBERPSYCHO, it doesn't matter where in the map. Whenever you approach the area, you'll receive a call from Regina. In may case, I received the call for the psycho and the call for the reward of the quests I did hours earlier. I can not guaranteed it'll work for you, but to me that worked, after trying any other method (reboot, hard stop etc). With the patch 1.04 this shouldn't happen anymore (to me it didn't and I was able to clear Japantown way more easily). I still have those 5 quests stuck in my journal, but the achievement popped and I got my rewards.
Hope it may help someone, happy hunting!