Once you reach 40+ age, you do more damage, but you become a glass cannon. So everyone's health drops mad fast. Once you defeat a certain enemy, you will get the elevator card key, and can go just straight to the boss if you want on your next run.I have to say I found the museum level remarkably easy compared to the club. Not that I finished the museum, but starting it at age 56 I was kinda mopping the floor with everyone.
I finished the museum at 31. I got to the second phase of the boss for stage 4, but I died until game over. I do recommend that you bring a weapon with you when facing these bosses. Makes things much easier. Also, there is cool mechanic where if you break a bosses stamina meter and press TRI+ CRCL (like you would with any mook), the fight will automatically go to the next phase. If you do the same during the second phase, the boss automatically dies.