Potion Permit

Every Single Villager that resides in Moonbury [this includes everyone in the "Social" tab of your journal] can be befriended and count towards this achievement. Friendship comes in 4 levels and is indicated by the smiley face next to the meters each character has in their journal Entries. they are as follows:
Level 0- Blue Face
Level 1- Green Face
Level 2- Yellow Face
Level 3- Heart

you can raise the Friendship of a Villager once a day by either speaking to them, or giving them Moon Cloves with the latter being a substantial boost. once you fill a friendship meter fully it Locks, and you must pick up that character's story mission from the Community Board and complete it to unlock their next tier.

you can earn Moon Cloves by completing some quests. you earn 2, once, for each side job as a milestone, and you are always given one each time you properly Cure a Patient.

As you can only reach this level with someone with the tag "Romanceable" in your Journal only the following Villagers qualify to earn this:
Leano
Martha
Matheo
Reyner
Rue
Xiao