Best strategy for getting a lot of GRADE
Defeating bosses get the most grade, so I would recomend doing S rank quests that you think will have a decent boss, kill it, and get the grade. If you have gone all the way to the last few storyline boss battles, that will be the best way. If you can't do any more quests, fight through the colosseum. You will get grade, possibly level up, and get manuscripts to level up your pets. You will not get much grade per battle, but at least you get something to aim for (the manuscripts, items the enemies dop) instead of just running into the same monsters all the time which will get very boring. Since there is no way to check your grade in this, whenever you think you have enough, fight the last boss(es). That should give you good grade. If you go through the colosseum, tell me which type and rank crossbones (the monster) is in.