Expert Team achievement in Fuga: Melodies of Steel 2

I don't know if this is strictly unable to be done on your first playthrough, but I think it'll be extremely difficult. Most of your XP will come from battles, but you can boost it further by achieving an S rank (1.5x XP multiplier for that battle) and by cooking and eating the dessert foods from the messhall (the bottom items on all food lists, higher level desserts increase the multiplier).
Expeditions provide some xp to the selected 3 children on it, and there are no unique abilities between the characters during the expedition, so pretty much always choose the lowest level characters available unless you really want to boost a particular character.
During the intermission, every action taken where you don't select characters will give XP to the controlled child, so switch off to lower level children when you can. You can also give up to 6 children (depending on the bunkbed level) a set amount of XP through sleeping, and achieving the notebook goal (think it's done by doing 5 children's requests) gives a sizable XP amount to all children. Finally, the golden pawbun in NG+ shop doubles XP gain from all sources.

At certain levels, the character's skills will also level up. Eventually, the skills will level up to level 3, which should unlock Skill Master.

Edit: Forgot to add that answering quizzes correctly also give a sizable amount of XP to the selected character. This can be done once per chapter after the generals join (think it was chapter 3). I'm not 100% sure, but I think if you get the quiz wrong, you can try again on the next intermission. Doing this 5 times also nets you Quiz Master.