did you do the 2nd ape fight?

also for me the achievment triggered on picking up the whiskers of the koi, for some reason.

1. You can google which bosses are required for this achievement.
2. You MUST use the same saved game file to attain ALL these bosses, main and mini. To do this, you will have to, say, after getting the Shura ending, you start a NG+ game, or NG++ game if you miss out any. And the way to verify that you have defeated the relevant bosses, go to the ingame menu and then Inventory and then items. Every time you defeated a boss, you will receive a "remnant" of that boss. If I remember correctly, the Man without Equal requires 14 or 15 remnants of these characters.
In NO way you should ever start a brand new game from scratch if you are going for this achievement.
In addition, I will advise you checking your Steam account status before starting the fight with any of these bosses. Make sure that your Steam account is ONLINE. There is a random bug with this issue. In other games, you can play offline since the game is a single player game and you can avoid poor internet connection by playing offline. And whatever you have achieved, the next time you go online again, everything should be resync. Unfortunately, there is a bug between Sekiro the game and the Steam client. This issue was acknowledged by both FromSoftware and Steam Support back in late 2019 or early 2020 (you can search this forum where the Dev. was online helping the person who posted the problem). Both parties couldn't solve the problem and the final result was that both were blaming each other. I was one of the observants. At the time, there were problems with the Steam Client which resulted in Steam account going offline without player's realisation. In any case, your chance of getting response from either party is close to zero now. Therefore, you can only do whatever to avoid this situation to happen. One way is to backup your Sekiro saved game files manually. I suffered the problem myself after spending a few days trying to defeat Isshin the Sword saint. With the backup, I didn't have to play the game from scratch. Still, I had to face him again though eventually I got the achievement.
Hope this help. Good luck and have fun :) The game is worth it. I still played it after 3,300 hrs :)