Also known as Gem Gem Monster, this is a kind of monster-raising RPG, but without the RPG part. The world map is more of a fancy menu, and most of it's non-functional. According to a guide I read online, you can give items to your monster and that'll open up new map areas, and even a whole side quest about collecting five special items. But whenever I gave the requisite items to my monster, nothing happened.
So what does happen? The game starts with you being told that you can make a monster by putting a gem in a can and shaking it. Surprisingly, this is actually the case! From there, the main thing you do is go to the arena to enter four tournaments of increasing difficulty, and also grinding to get strong enough to win the tournaments. There really is an insane amount of grinding in this game, and I strongly recommend you have a fast forward button mapped to a convenient button (since I assume you'll be emulating it).
It's not a completely mindless grind, though, and this is thanks to the relationship between monsters, gems, and moves. Gems are turned into monsters, that's already been established. But gems are also moves, and there's a bit of proto-deckbuilding in here, since you've got to maintain a deck of twenty moves for your monster to use in battle. Every turn in battle, you can pick from your current hand of four, and the one you choose will be replaced by another random one from your deck.
When you're not at the arena, you can also go to the fields, and turn a gem into a monster for your current monster to fight. Most of the early gems will just drop a copy of themselves after you beat them. This is useful if you want to build up a bunch of useless gems to sell, but it gets more interesting a bit later, when gem-summoned monsters start dropping slightly more powerful gems after you beat them. So, this improves the range of moves you can put in your deck, and it also gives you access to better monsters.
I think that your monster is actually just an incorporeal spirit, as when it's defeated in battle, it dies, and you pick a gem from your inventory to turn into your new monster. But your "new" monster has the same name, experience, and maximum HP as the old one, so it's more like reincarnation? Their attack and defence stats will be determined by their new form, though. Frustratingly, you don't ever get to see what the attack and defence stats are, though, so you just have to assume that a gem that represents a stronger move also represents a stronger monster.
Lil' Monster is a game that's all about boring grinding with a little bit of strategy, and a clear path of progression to string you along. Being on a handheld definitely helps its tolerability, but honestly, there are many more interesting handheld games about grinding if that's what you want, and plenty of even more interesting handheld games that aren't about grinding, too. It's better than Wolf Simulator, at least, but that's not saying much. The main reason I stopped playing after several hours, though, is getting eternally softlocked in a battle where my opponent healed every turn, and my own monster wasn't taking any damage at all for an unknown reason. So if you do decide to look into this game, save often.