Can someone fill me in on the story and what it's all about?
I can't find anything related to the storyline and the progression throughout the game
(I'm too stupid to play it myself and I don't want to use a walkthrough)
I don't know if that is sarcasm or not, but to answer your question: No.
Although it's heavily Indiana Jones inspired, it has nothing to do with it.
It's a Metroidvania style game with no linear path towards the end, exploring the ruins of La Mulana and the outskirts of it, collecting Items and Upgrades and progressing through a series of trails and puzzles inside the Temple with Enemies and Bossfights.