This suggested sequence is for people who are more interested in the life skills like components and are not interested in ranking up mana crystallization at the early stages of Alchemy Mastery.
Alchemy Mastery Wiki Link: Alchemy Mastery - Mabinogi World Wiki
Practice to Rank D alchemy
Learn Barrier Spikes and rank it along the way, preferably to rank 5+. Do all the crystal making requirements.
Rank C and B alchemy
Water cannon to Rank F. Do the crystal requirements and the attack requirements.
Rank A alchemy
Along with crystal requirements, go through all the attack requirements by using Water Cannon for about 800-900 times.
Rank 9 alchemy
Call a golem or barrier, with the same-enemy attack requirements.
Some synthesis is also needed.
Rank 8 alchemy
Defeat same-level enemy for 800 times along with calling a golem or barrier for the rest of the requirements.
Rank 7 alchemy onwards
This is probably where the hard part starts. Bulk of it might have to come from attacking. Rank 2 is also dependent on mana crystallization.