Mission 1: Found
To find the first key, head to the left of where you take out your first Lost Soul and hop across the platforms that lead out to the small area. When you reach the end of the path, the key will be waiting for you there
When you enter the funhouse, make a left at the wall of eyeball paintings and run towards the mirror at the far end. Before you reach it, make a right and the door will be in a hallway there.
Mission 2: Home Truths
When you are in the first large room, go up the stairs and head to the right. Continue around and inside the door way at the far wall will be the key.
This key can be found just after you get the arbiter from the painting. When you proceed down the hallway and drop through the floor, there will be a red jewel on the ground that you will need to smash with the Eryx. Smash it and the key will be in the floor
Immediately after you are shown how to use the demon pull, you will drop down a hole in the floor that has a red jewel on the ground. The door will be to the right of the jewel and in plain sight to see.
After you receive the Osiris from the painting, you will then need to head back outside and cross some platforms by demon pulling them. When you reach the far side, you will need to smash through a red and then a blue door. Once you do, look to the right to see a large gap with the lost soul at the far end. Air dash across to reach it.
Mission 3: Bloodline
At the start, after the battle with the Ravager, go forward to the door opening, but before going through, make a left down the corridor. Smash through the red door there and follow the stairs up to find the key at the top.
In the main area where you begin, you can reach the Argent door by making an air dash (once it is acquired) from the upper walkway to the platform that the door is resting on.