The Alchemist is an unseen character on the island. He intended to develop a cure for the Malaise, though his efforts appeared to all be unsuccessful.
It was implied in the description of the Guardian's Haven that the Alchemist was rather unpopular.
"The Giant didn't like the Hand of the King, and the Hand of the King didn't like the Giant. But they did agree on one point: nobody liked the Alchemist."
Some soldiers sided with the Alchemist against the King. In the Forgotten Sepulcher, one of those soldiers, who was in direct contact with the Alchemist, built a secret lab, presumably to do experiments related to the Malaise.
"I realize the risk I'm taking by writing this letter. The King's methods are getting us nowhere and the situation is deteriorating. We have to switch a more peaceful method immediately! I've spoken with the alchem..." — Letter found next to a clandestine lab
In the Toxic Sewers and Ancient Sewers, the Alchemist was collecting mold and mushroom samples for his experiments. However, the undead creatures were getting in the way and so he presumably ceased his attempts here.
"It is becoming increasingly difficult to collect mold samples in these sewers. There are too many revenants."
In the Promenade of the Condemned:
The Beheaded mentions that the Alchemist was very "thorough" upon inspecting the insects next to this grimoire.
The Alchemist was applying a substance found in the Sanctuary on bones from corpses, likely executed prisoners. The substance's effects were unpredictable and the Alchemist reflects whether his experiments are worthy or mass murders from the king are more effective.
"The sanctuary substance produces unpredictable results on the bones I've collected here. All these bodies... All these lives. At the end of the day perhaps The King is right?"
About the bodies next to the grimoire, the Beheaded mentions it's:
"Hard to say whether these bodies were infected. But one thing is for sure: their skin melted like old cheese in the sun."
The Sanctuary seems to have been especially important to the Alchemist's research. It's the only biome that contains two different Grimoires.
According to one of his writings, people believe the sap flowing through the walls of the Sanctuary is responsible for the Malaise, by contaminating the sewer network. He also hypothesizes that as a potential cure. He harvested and used this substance as part of a treatment for the infection, as indicated by the Grimoires of the Ossuary and the Clock Tower.
"Some say the sap that runs through the walls is flowing into the sewer network and causing the Malaise. But perhaps the problem can also be the solution?"
In another Grimoire, the Alchemist references the Time Keeper's efforts to combat the Malaise. He implies that she is manipulating time to contain the Malaise, but that her spell cannot contain it forever.
"Time is running out... literally. With all due respect, she cannot contain the Malaise forever"
"The bodies immersed in the latest solution are changing less quickly. I must extract the essence of this solution and apply it to other volunteers"
The Alchemist was also researching the Malaise in the Forgotten Sepulcher, but the bodies kept resurrecting themselves and the Darkness was making his work difficult for reasons yet to be specified. These prompted him to leave.
"The bodies have woken up again. And this darkness... I can no longer continue my experiments on the Malaise here."
Additionally, there is a lab in the Castle destroyed by the king's loyalists, all of which criticize The Alchemist's efforts for creating a cure, and that isolation is more effective.
The Alchemist was using the crystals mined in the cavern in his experiments to slow the Malaise's infection, as evidenced by a body immersed in a crystal solution next to his grimoire.
"We can do more with those crystals than sell them, I'm sure of that. Using them on corpses doesn't do anything for now, but I have to keep going!"
- Re-translation of the original French. The English translation loses the pronoun she and therefore the meaning. In the original text, it is very clear the Alchemist is referring to the Time Keeper.