This is the highest difficulty in the game. Enemies scale up with you (Can't bulldoze your way through them), hit hard and can take tons of damage before dying. Watch out for the grimmocs with spinning attacks, the shamans and the ones with the crossbows in particular. They are fierce with their attacks and almost always appear in groups. Small enemies should not be underestimated, either, as they can eat away your health if you're not careful, so be ready to dodge as many attacks as possible by rolling.
Make sure you do the side missions for the item upgrades before playing on deity difficulty, cause you'll definitely need lots of potions and totems, with some smart bombs for good measure. If possible, save them for boss battles. (This is why playing solo isn't recommended)
Certain bosses are easier than others. Like in my case, the Ice Elemental and Sundrax didn't pose too much of a challenge, nor did the 'battle' with Gloria (The ship). But others like Zane and the Tallicus beast were rather difficult due to their multiple phases. If enemies appear during the battle, at least one person should kill them before they become troublesome, if there's 3/4 players in the lobby. If not, juggle the duties while whaling on the boss.
I highly recommend you play with at least one other person so they can revive you in a pinch, but more is always better. (More chances for survival in the tough boss battles, plus sometimes randoms can drag you to victory
) The missions can be done in any order, and as long as they are 'colored in' (They start off with a grey color), you should unlock the achievement. I joined some missions halfway or late a few times, and it appears to count that, but try joining during the beginning to be safe.