Gurumin: A Monstrous Adventure is a must buy, it's my best PSP ever.
Gurumin is a action adventure RPG/Platforms hybrid (yes there is almost everything here) it might remind you for some N64 platformers, Zelda and Megaman Legend but it's more than that, as it got it's own identity and is full of souls and charm.
The combat system is not shallow and require skill and you can feel badass doing the jump attack if you get your timing right, aside from fire and ice lightning for your legendary drill there are tons of upgrades for for Parin outfit, game can be very challenging in higher difficulties but the easy mode is good for new comers. There is platforming in Gurumin and it's pretty good and also hidden collectables and lots of secrets and dungeons ( to beat and to break your record and to discovers hidden paths) plus puzzles and some funny mini games.
also It got really awesome cast, funny and strong female lead (Parin) with awesome cast from a blob dancing thingy to a big blue legendary cat and it's a voiced PSP game, the story is also is sweet and get dark later on and you'll need to beat every dungeons to get the true ending which will make you cry (both endings are "good" by the way).
and for icing on the cake? it look awesome on Vita and with mapping L/R to the right stick for camera controls it remove PSP platforming camera control issue and play better on Vita.
^ it even better looking than some of the recent Vita games
buy it.
*sorry European guys*