The best action games like The Legend of Zelda The Minish Cap are The Legend of Zelda: A Link to the Past, The Legend of Zelda: Link's Awakening and A Link Between Worlds. Below are 6, each with the reason it is here — and, at the end, what filtering to action costs you.
Filtering to action means you want the fighting to carry the game rather than the story or the map. It is the right filter when what you actually miss is how something felt in your hands.
What you get: Combat you get better at. Action games put their design budget into the moment-to-moment, so the thing you are doing in minute two is the thing you are still doing in hour twenty, only better.
What made The Legend of Zelda The Minish Cap worth playing in the first place is covered on the full list. This page is the action part of that answer, and only the action part.
The template, and the two-world structure Minish Cap plays with.
The most charming 2D Zelda, and the remake looks superb.
The 3DS entry, and the closest in feel to Minish Cap.
Compact top-down adventure, paced like a 2D Zelda.
A straightforward, well-made 2D Zelda in everything but name.
Wordless top-down adventure with a striking look.
Pacing and world. Action games rarely have the quiet stretches or the writing that the adventure and RPG picks bring, and a few of them are shorter than they look.
Specifically, these are strong answers for The Legend of Zelda The Minish Cap that are not action games, so they are not on this page:
The full list is on games like The Legend of Zelda The Minish Cap — 9 picks, no genre filter.
The Legend of Zelda: A Link to the Past. The template, and the two-world structure Minish Cap plays with.
No. The Legend of Zelda The Minish Cap released on the Game Boy Advance, but a recommendation is only useful if you can play it, so the picks above span platforms and eras. What they share is the genre and the reason.
A small set of verbs and a game that keeps finding new questions to ask of them. The weak ones add buttons instead; the strong ones make you better at the ones you already have.
No, and difficulty is a poor proxy for depth. Some of the hardest action games have very few decisions in them, and some of the deepest have a difficulty setting that lets you meet them halfway.
By hand. Each pick was written for the full The Legend of Zelda The Minish Cap list first, on what the game actually does, and this page is the part of that list that is action — never a genre tag lookup, which is how "best racing games like Super Mario 64" used to be a page on this site.
Or read the action guide for where to start in the genre generally.