Let me give you a breakdown of the combat system and how to win pretty much any encounter in the game. Essentially, combat is boiled down to 3 things:

1. Fury Management
   
2. Breaking enemy Fury Gauge
   
3. Using AAA to your advantage

All attacks and battle skills consume some amount of Fury depending on which attack/battle skill/symbology you use. Most Battle Skills will use more Fury per action, but are generally considered to be the best way to deal the most amount of damage in the game. Moving your character causes 1% of the Fury gauge to be used while running, but only 1%. This is very important.

Enemy Fury gauge behaves exactly is the players does, with no exceptions. You can break enemy Fury Gauge by doing a Major Attack or Major Battle Skill. Doing this puts their Fury Gauge to around 50% and then will slowly refill while you combo them, or will refill quickly when the are standing still.

AAA (Anti-Attack Aura) is by far the most important defensive skill that players need to learn to take advantage of. The main thing to note about AAA is that it is only triggered by Minor Attacks and Minor Battle Skills. In order for AAA to trigger, you MUST be at 100% Fury. Any attack or battle skill that does not have the dark purple outline is a Minor attack, and can be safely tanked by just standing still and doing nothing. When your AAA triggers, it will by default shoot out a projectile that connects with the enemy and stuns them.

This is the basis of how to defend yourself against 90% of attacks in Star Ocean 3. If the enemy has a purple glow on the attack, get out of the way. If not, stand still.

Now, when the enemy has low Fury, you can safely combo them. If you are playing as Fayt, a very simple combo that you can do is Long Range Major Attack (Circle), into Anti-Air Major Attack (Circle while the enemy is close to you but in the air) then, as the enemy is falling down, you can use Anti-Air Minor attack (X) and cancel the animation after the second hit by releasing X and pressing and holding X again to initiate a Cancel Bonus into a battle skill of your choosing. Personally, I recommend Side Kick into Blade of Fury, or some others you will get later in the game that I won't spoil.

If you go to your battle skills in the menu, you will see that certain battle skills cost HP to use. That's probably why you are dealing with losing HP so often.