Valkyrie Profile is an experimental game, and like so many experimental games has elements both brilliant and befuddling. Ultimately it tries your patience a little too much by being too heavy on the level-grinding, asking you to manage too many obfuscated and unruly systems, and having too many obscure yet important missables that you'd never discover without a guide. But it's certainly interesting, even if exactly how "good" it is on the whole is debatable.
First of all, this was originally released on the PS1 in 1999, with the PSP port not coming until 2006. It's pretty much a straight port, with the only major additions being a redone script apparently given a more literal translation from the Japanese (though the original English voice acting is retained and their dialogue lines are not changed) and a few incidences of censorship (such as pentagrams) restored. There are also all-new CGI cutscenes in the style of FF8 that take the place of the anime clips used in the original game.
If you're entirely new to the whole thing, it's Norse mythology ported over to an original world in which you step into the shoes of Lenneth, a mid-level god working as a foot soldier for Odin. Lenneth's job is to locate and recruit the recently-departed souls of worthy humans for Ragnarok, the ultimate battle between heavenly forces that apparently has snuck up on everyone and will take place in only a week.
So the game is divided into eight chapters, and time is kept in units called Periods. The game doesn't pass in real time -- you burn Periods for entering locations on the world map, and usually have an allotment of 24 periods per chapter. Entering towns takes 1 period, entering dungeons takes 2, and stopping to heal the party up can take from 1 to 3 depending on how thoroughly you want to restore them. But in order to find the human souls you require, you need to use Lenneth's "spiritual concentration" ability, which unlocks both the characters you can recruit and the dungeons you'll need to visit to power up your characters and retrieve Odin's stolen artifacts.
Aside from doing it for basic survival, you'll also need to train your party in order to make low-level gods out of them and pack them off to Valhalla to fight the unseen (and unplayed) parallel war going on between Odin and rival Surt. You can transfer up to two characters per chapter, but usually only one is needed to get the best ranking and get the biggest haul of goods from Odin and his secretary Freya. Freya leads off each chapter by giving you a list of requirements needed in their current hero du jour, so you'll want to train up the right sort of character based on what they ask for -- sorceror, swordfighter, archer, etc. But you also have to consider each character's personal attributes. When each character levels up, they get skill points that are used both to raise their statistics and learn new combat abilities, and also to improve their character traits to make them more heroic and worthy in the eyes of the gods. Sending up characters with the wrong traits doesn't really do much beyond reducing the amount of points and goodies you get in return, but sending up a character whose "Hero Rating" is lower than required can lead to them getting perma-killed in Valhalla. Which makes you feel like a dick for not giving them a proper education.
On the world map, you fly about in a style somewhat reminiscent of Actraiser without the civ-building elements. You use "spiritual concentration" to locate a character, then fly to their town to watch a vignette that usually resembles a tragedy of classic literature much more than the typical Japanese animu hijinks. This is not the game to play if you're in want of cheering up, as every character you recruit requires watching their death first, and most of them die badly -- some of them like literal dogs in the street. The world of Valkyria is cruel, hard and despairing, somewhere between Charles Dickens and George R.R. Martin in composition. It feels like a world that's about to explode under the weight of its own petty, shitty inhumanity.
Unfortunately that severe attitude seems to have extended to the overall design philosophy, as well. Valkyria throws you into its world without adequately explaining many of its elements, leaving you to just learn by experimentation (and more than a few system resets after unwittingly burning Periods to no purpose). The game is a somewhat dizzying ongoing process of leveling characters, creating new items, equipping the best possible items to optimize combo attacks in battle, transmuting existing items into better items, using stocks of XP granted by finding Odin's artifacts to quickly and strategically power-level characters, and keeping on top of your main character recruitment and Valhalla transfer duties, and the somewhat scanty tutorial dungeon at the outset doesn't cover nearly enough of it.
Even when you do understand how all the menu-based subsystems work, Valkyria still trips you up with obscurity continually. You quickly learn by experimentation that visiting towns is a waste of Periods unless it's been indicated to you that a character is there, since there's nothing to do in them ... with ONE isolated exception needed to begin the confusing "A Ending" chain that actually contains most of the game's main plot! Another requirement for this chain is that you play on Hard difficulty ... not only is there no in-game indication that you'll have to replay the whole 30-hour game to see the actual story, the game actually actively dissuades you from picking Hard mode with its description of it in the opening screens!
Aside from the game's main plot being buried behind a chain of insanely obtuse events and requirements, the dungeons also exist as discrete entities that never seem to have any bearing on the game's main story. They're just some random Pit O' Evil that appears from time to time while you're looking for characters, and serve no purpose other than as the only place to level your characters and to recover the Odin artifacts that grant you tons of XP from the boss . The dungeons sometimes contain their own interesting little isolated vignettes similar to the tragic mini-stories of each of your recruits, but had there been another means of leveling there would be no practical purpose to ever entering them in terms of the game's greater overall narrative structure.
The "Periods" system might initially make you think that time management is going to be a huge part of the game's challenge, but that's actually only an issue in the very early going when you don't know what the hell is going on. Later chapters find you with very little to do and as much as half your Periods sitting there for use on nothing more than level-grinding in dungeons you've already completed and looted. You'll find out you need to do that tedious level-grinding, though, or tough bosses in the next chapter will absolutely smash the shit out of your unprepared ass.
After all that complaining, what's good about the game aside from its unusual-for-Japan Homer/Shakespeare-ian tone? Well, it looks really nice, for one. Well-done sprites with detailed animation, detailed portrait backgrounds with parallax scrolling effects, and portrait art that makes characters look more human than the usual shonen anime idiots. It's also got a soundtrack done by Motoi Sakuraba in his keyboard-soloing peak, and I think it might be my favorite out of his work that I've heard so far. It also has an entertaining action-tinged battle system that helps leaven the grind a bit -- characters will attack differently with different types of weapons, and you have to time their strikes properly to break the enemy's defenses and rack up big unblockable combos.
As I said at the outset, however, it's an interesting game. It was experimenting heavily, and the experiment didn't entirely come off, but did enough that I'm now curious to play the later games in the series to see how they built on these ideas. The game is at least worth a shot for period RPG lovers, as if you end up digging it to the point of wanting to play it multiple times it has a lot of meat to offer. But the obscurity, complex unexplained systems and general difficulty is likely going to run off everyone but fairly hardcore JRPG vets.