First and foremost is entrance into the Alchemists' Guild, a 10 pt advantage - counting as a Patron which makes equipment, component and workspace easier to obtain.

Next is learning their secret language, the Alchemical Lexicon, a M/H skill, in which all formulas are recorded.
Alchemists are sworn to their Guild, to never reveal a formula. Then comes the Alchemical Technique (M/VH) which is the art of using the equipment itself, along with the formulas of a few elixirs.

An Alchemist is an expert in making a number of Elixirs equal to his Alchemy skill, any others spell WITH A FORMULARY to work from, are made at -2.  For any elixirs for which he lacks a formula, it's pure guesswork, taking weeks, huge amounts of money, and a roll at -5.

Alchemists can make all of the standard GURPS potions, but with different names, of course. They may be more than one way of making a potion.

Example:  Hermes, Potion of Stealth:  Stealth and Climbing +1d for one hour. $300 to make, 3 weeks, -1 to skill

Azshia's ThiefAide, same effect,  $100 in herbs, still water collected while HandMaiden is at zenith, a thief's toenail, 12 live spiders captured either in a treetop or building over 100' high, the voluntary oversight an owl, a smoky quatrz carved in a celtic maze pattern. Ingredients added over a period of a week. NO noise must be made during the entire process - the room must be silent and the Alchemist must take a vow of silence. This takes a will roll each day at +1per day in process (Thus will +3 on the third day). -1 to Alchemy skill. May be made in batches - separate Alchemy role for each one at -1 per elixir over two.