1. Be sure to stock up on dampeners. Make sure to use them in boss fights whenever a boss draws in power. Lots of times they'll use their strongest move at this point, so it never hurts to put up a dampener of that type to waste the boss's turn (Like Hydra will use toxic breath, which is a dark move during its magatsuhi turn. Use a dark dampener and you'll take no damage.)

2. Be sure to fuse frequently, and don't get attached to most demons. Fusion is the best way to keep up with the game. You get to keep moves you want, you get a wide assortment of demons at your disposal that tend to have higher stats and better resistances than you currently have, and you get the ability relatively early on to carry over stat increases and levels when you fuse. This isn't Pokemon, it's not generally a good idea to keep an early game demon to the end game unless you're looking to challenge yourself.

3. Swap your affinities as needed. Most bosses specialize in a particular element or two, try to find essences that resist or at the very least aren't weak to what you're fighting. A good example is Daemon for Hydra as he's resists fire and is immune to dark, making the protagonist not have to worry about some of the Hydra's strongest moves.

4. Don't forget the buffs! (And debuffs). SMT is a game series where buffs and debuffs matter, no enemy is immune to it and they're guaranteed to hit. Generally it's better to debuff in the early game due to the lack of multi target buffs, not to mention any debuff done to a boss affects your entire party. Ailments are also important too, while most bosses resist all ailments, almost none are immune to all. If you have a spare turn, you might as well go for a seal, charm, or sleep to make things a lot easier.

5. Magatsuhi. Critical is strong, but it's not the only one. Feel free to experiment a bit, some are better than others, but almost none are completely useless. Make sure to get the talisman first if you want a specific race's ability. You'll find talismans from completing quests, collecting Miman, and even talking to regular npcs, so make sure to talk to everyone just in case. Later on you'll get an ability that lets the protagonist use Magatsuhi skills of anyone in his active party so it can be handy to have a wide variety of demons of different races, even for just the ability alone.

6. Try your hardest to avoid having light/dark weaknesses on your main character. Instant kills exist in this game, but they generally only have a chance to instant kill if you're weak to light or dark. Your main character is weak to dark by default, so a stray mudo can instantly ruin your run if it happens to instant kill proc! I'd recommend switching affinities just to be safe, as if the protagonist goes down, that's it. Game over.