The best action games like Castlevania are Super Castlevania IV, Castlevania Symphony of the Night and Ghosts n Goblins. Below are 10, 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 Castlevania 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 same game loosened up — whip in eight directions, and the atmosphere intact.
Where the series stopped being stages and became a map. The other half of the genre.
The same era of unforgiving, pattern-learned platforming.
The other NES action platformer built on memorising a level until it becomes easy.
Faster, meaner, and the wall-climbing gives you options Simon never had.
The modern continuation, made by the producer of Symphony of the Night.
Heavy, punishing, religiously ornate — the tone taken seriously.
If the map rather than the stages is the part you want.
NES platforming rebuilt with everything learned since, Castlevania included.
Same console, same pattern-learning, guns instead of a whip.
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.
The full list is on games like Castlevania — 10 picks, no genre filter.
Super Castlevania IV. The same game loosened up — whip in eight directions, and the atmosphere intact.
No. Castlevania released on the Nintendo Entertainment System, 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 Castlevania 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.