@Rhalerien - You were 100% correct for the Monarch. Thank you! I guess I just didn’t pick the one choice.
Also, I did find a way to get the Portrait of Melmoth, so your hints helped me narrow down the area, though I had to go a different route. What I ended up doing:
First, this is dependent on you actually having a low Insight. Then, when you try to get into the ball choose: I will flag down a carriage and try to persuade its occupants to allow me to join them.
Note: You don’t want to recognize the lady in the first one, the Scavenger’s Daughter. So don’t get chummy with Mona (who knows her) and keep Insight low (otherwise you recognize her). You will eventually get into a carriage with Melmoth, but he is masked. Then when you go into the secret room, you will see a portrait of him and get the Achievement.
Black Mass is a little involved.
This one occurs after Holofernes directs you to procure a fresh corpse. Choose to Enter the Catacombs beneath the Necropolis (this also leads you to meeting the vampire).
The key here is that you need to enter, but then get caught by the cult entering it. Choose: I will conceal myself within the Necropolis grounds and wait for night to fall. You need to be found, and need a low Crime value (to high and you will avoid it).
Coming of Age
This one occurs near the end. I don’t know if it is necessary, but there is a part of the Mocata House mentioning about the Thallo secret, and asks ‘Is it worth the price’ and I reply ‘Yes’.
However, I think you also need to find pieces/clues along the way. This part is just speculation on my part, but when you go to the ball choose to Investigate the Cabinet of Mysteries. You will come across a Monk looking for his heart. If you find his heart, then he will give you a good history/rundown of the Thallo’s.
It might also be helpful to have a high Occult. This way, if you then search: Lord Thallo’s collection of occult literature, that will give you more information. If the above suppositions are right, when you meet Thallo, the achievement should automatically trigger
Please be aware that I might have included some unnecessary steps in the above, so others might have some better insight here.