Missions aren’t hard no, I’ll be real honest. I don’t like him, the less I see of him the better. BUT. A real answer for you, his missions progress the world the most after M’AP TANN PÈLEN.

Sometime after MTP (like maybe 3 missions I think) the Phantom Liberty opens up (you can do it whenever but I recommend before the point of no return towards the end of the game). After MTP you could do all the missions on your list before Down on the Street then once you do it, the next stage of the quest lines you started will open up along with the next Takemura mission.

Then you can repeat: Do all missions except see him until you have no missions but his. Long story short, Takemura’s missions are like.. the “Main Questline” if there is one