Basically, you need to talk to characters in the game - all of them!

Sports and Superstitions
The Mysterious Locket - give Locket you found in Celestial Shrine to Liza
The Missing Manga - talk to Vesper
Pretty in Pink - talk to Lux
Emrys Academia - talk to Rainy
A Research Expedition - it's actually puzzle quest given to you by Cerisse
Horace's Training Camp - fighting quest by Horace
A Strange Acquaintance - Easily missable - you must choose to go with Cordell on the train & not with Liza
The Secret Letter - they are written by the King
Puzzle Master - you need to complete every puzzle in the game, they are easily missable - in the forge, in the creepy shrine, in the starting shrine, in the study shrine, their location isn't marked
Collector - you need to complete every quest to get this, complete every puzzle & pick every item of the ground - it's only awarded at the end of the certain boss battle
follow this guide for Collector achievemets. https://gtm.steamproxy.vip/sharedfiles/filedetails/?id=1707509123

You get these naturally, by going through story:

The Traveler
Welcome to Emrys

these are battle related, but unmissable
Star Dancer
Nightmare
Knuckle Up
Heating Up

Other battle achievements that might be easy to get, but don't know how missable are they:
Ember Adept
Strike Adept
Skock Adept
Cure Adept
Void Adept
Essence Adept

Battle achievements that is PITA to get for soem reason:
Human Savers Club