You play as Wylfred. Wylfred and his family suffered through a long draught and watched his father succumb to starvation. He witnessed the valkyrie, Lenneth, take his father into the afterlife and assumingly blames Lenneth for his death. As Wylfred grows older, he becomes more bitter and curses the valkyrie's name on the battlefield. In your first battle, Wylfred dies and in his astral journey is confronted by a servant of Hel (the person, not the place.)
The servant, Ailyth, tells Wylfred that he can be restored to life if only he promises to one day kill the valkyrie, Lenneth. In his swiftness to agree to the faustian proposal, he agrees to something more sinister. In order to confront Lenneth, he was given a feather called the "Destiny Plume" and he must stain it black with sin. (They mean sin in a metaphysical sense and not a moral one.)
In order to obtain more sin, Valkyrie Profile: Covenant of the Plume insists that you earn it in one of two ways. You can either "overkill" enemies by continuing a combo or attack even after the enemy is dead. Or you can earn sin by one of the most conniving gameplay devices I have ever seen in an RPG; you have to kill your party members. That's right; the most efficient way to meet your sin quota is to sacrifice your party members to the plume.
It wouldn't be nearly as bad as it sounds if you weren't at such huge disadvantages so often because you didn't meet the required sin quota from the last battle. At the beginning of every battle, you are given a set number of sin that you must reach, and if you reach it then you are rewarded handsomely. If you fail to meet the requirements, you are warned once and then subjected to ethereal doppelgangers of your party members that are much higher in level that you. By choosing a victim for the plume, that person essentially becomes immortal for the remainder of the fight and can easily dispatch the remainder of the battlefield by themselves, which, unfortunately is one of the only ways to kill the enemies that are sent when you don't meet sin requirements.
Battles take place on a traditional grid-based battlefield and each side takes turns advancing and attacking. When one of your party is ready to attack, it takes you to an actual battle screen where whomever is allowed to attack follows. Each of your party members is assigned to a face button and that allows you to attack in combos or chains to maximize damage. This is why you can only have four fighters on the field at any given moment, one character for each face button. (But it has no problem sending 10 enemies to fight you!)
After an enemy is defeated, you are immediately rewarded with experience and items afterwards while still in the bigger battle at large. So it is possible to level up while still trying to whittle away the last of the boss's HP.
The last device that Valkyrie Profile: Covenant of the Plume utilizes to a somewhat successful effect is a branching storyline. It breaks away into three distinct paths throughout. Basically you start on the righteous path, and as you sacrifice more party members to the plume, you fall into the next level of the path until you can see a Game Over screen for killing too many allies.
I feel tired now having to explain so much before I can give an opinion that will seem just. Valkyrie Profile: Covenant of the Plume is incredibly deep and complex. There are so many systems operating at once, it is almost daunting. However, I feel that it goes too far into narrative-driven gameplay devices, (i.e. The Destiny Plume.) instead of focusing on the really fun combat systems. I understand that many RPG enthusiasts only play that genre for stories, but fun combat keeps me coming back to find out what happens next. By giving you very one-sided decisions in whether or not to use the plume, I feel like I miss out on a really interesting side story. A story that was cut short because I had to sacrifice an ally in order to not be killed in battle, or in most cases, simply win the fight so you can progress further for the main story.