Demons don't need to just be beaten down you know, you can chat to them too. Though how far those conversations go depend on you and the demon. The fact is, some demons might not like your personality. In some cases, they might even outright refuse to talk to you. But when you do get a conversation going, keep in mind that while many demons just want you to flatter them and stroke their ego, others want to be challenged by a strong Dx2, and not a wimpy human.
Party up
Getting a strong party together is an essential part of the game, of course, so as you convince, summon and fuse demons, make sure the strongest ones are in your party. Your other Dx2s will also have their own demons party, and you'll even be able to swap between which Dx2 you want as your leader as you collect more. Make sure to swap between your Dx2s regularly, otherwise they won't get experience, and you won't be able to unlock new skills for them.
Planning each move
If you're coming up against tough battles, then you should slow down and take your time to ensure you're doing everything you can to win. Check enemy weaknesses you aren't aware of by using moves of that type - including physical melee attacks - and if there's multiple enemies, try using moves which hit more than one demon. If you hold any attack, you'll be given a more detailed description of what it does, who it hits, and more. Take your time to learn these moves, especially if you're not familiar with SMT games, to get a leg up in the fights ahead.
Still my turn
As you use moves that put your opponent in an awkward position, their turns will actually be pushed back. If you look at the top left of the screen, you'll see the turns you can take, with each turn you take taking away a chunk from the set of icons. If you use an elemental ability which you opponent is weak to, you'll only lose half a turn, instead of a full turn. Make full use of this to do as much damage as possible.
Weakness, resistance
The key to good results in battle is, like in many turn based RPGs, using elemental advantages in order to turn the tide of battle, of course. Using moves your opponent is weak against will obviously do more damage, but you have to avoid using moves they're resistant to. Some enemies will even absorb the damage you do of a certain element, and take it all as HP. Exactly the opposite effect of what you want, so keep an eye on the enemy's resistances and weaknesses on the right of the screen.
Having a chat...