it's in the sticky.
Max skills' events are unlocked after some part of the story (like listed in the sticky). To view the events Max can NOT be in your party. To remove him you have to go in his office in his base, go see the event, get him back in your team, go back to where the event was and get the skill.
Grand Marshal/Gladiator Priest, Lightplol.
PvE gladiator holy paladin, Lightp.
To be more specific:
after you beat Celcius the Ice Craymel his wife will appear next to the Van Elta (the ship/boat of the game.
Next time via the Gnome Statue at Tinsea (the town you enter before you fight Volt).
Lushika the town that you enter on the way to gnome mines (later in game)
The area where Reid and company first land in Celestia (later in game)
last location Jini Nightime to the screen east of the in later in game as well.
Then after taking to his wife in the above 5 spots go back to the same locations to learn those 5 moves BUT for the Tinsea Gnome statue one enter Shadows Cave at least once first.
Fighting Shadow himself isn't needed.
Chat 1 island nearest the spot where you first get he AI fish (subupgrade) has 1 move for chat another SE of Mt Farlos (in Inferia for another).
The other 2 are late game as well 1 via a subquest (go back to Chat's hideout) around the time that you can go back in Inferia to start this suquest.
Her last moves needs access so that the Van Elta can launch a airship to fly to the Hot Springs area (in Inferia for her final move) which can only be done once you can enter the final dungeon.