I can read Japanese but I'm not an RPG guy and lost in the game lol
The demo of each RGG always got a lentghy battle tutorial but this demo doesn't have any. I wish it was in the demo.
Combat is fairly straight forward at the moment. Main things to remember:
"X" is just your normal attack. No SP spent. Decent damage in the demo for Adachi and Ichiban.
"Triangle" Gives you your SP menu - so all attacks that use SP are listed here. Each different power is listed here for each character and class - so as you level up your character and class you get more moves. There's a variety of attack and stat boost moves for each character. Listed in the menu is the QTE followup commands you can perform if you get timing down right. Also listed in the menu is if it targets one enemy or has a area of attack effect (gotta say I like how detailed the menu is!
"Circle" is block, not quite sure why you'd want to use this command myself when you could just use an item or something to heal.
"Square" is items - it brings up a sub menu so pressing square again brings up your item menu and you can choose from healing items, stat boosting items (including stuff to remove debuffs like bleed, paralyze etc.)
Ichiban has an extra option in this menu - pressing square, then triangle brings up the summon menu, where stuff like GBH or Crayfish live!
In terms of the combat, when your on an enemy attack phase, when the enemy attacks you, you can do a defend move to half the damage they inflict - press "X" just before the enemy hits you and you'll defend the attack and take much less damage. Also, it means you won't fall down either.
When attacking enemies, you have a chance to knock enemies over when you hit them. They fall down easy. You can then follow up this attack with your next characters attack (assuming its not an enemy turn) and if you hit them while they are down you deal critical damage, which is fantastic! Other perks to attacking in certain circumstances are: hitting people into the road (and then having the enemies get hit by cars), attacking in highly populated area in terms of weapons and doing a normal "X" attack close to a traffic cone, bike etc. and you'll grab them to use for a damaging attack.
Restaurants and the heart healing area, as well as items give you health and SP back, shops let you buy better weapons for decent stat upgrades and each class changes your stats.
That's basically what I've picked up on so far. There's also stuff like allies hitting enemies when they are down automatically (they just need to be close to them, only happens sometimes), running at enemies behind other enemies may not go so well (the ones in front may attack you to stop you from reaching the other), running toward an enemy who is positioned behind bikes, signs etc. has a chance of you kicking the bikes etc. to smack them into the enemy, then you follow that up with your normal attack.
Oh, and normal attacks that aren't listed as having area of effect attacks can actually still hit other enemies if they are close enough, which is cool.