I'm not an Space Harrier fan, but I have been enjoying this.

The good:

-Nice stylish visuals and music
-I like the punching mechanic, it feels nice to punch your enemies
-It has (very basic) difficulty settings
-There are multiple paths. After finishing a level, you can choose between 2 options to move next
-It runs nice on my laptop

The bad:

-You can't remap controls
-Bullet time mechanic feels weird, specially the movement after you activate it
-For bosses, most of their bodies are immune to damage, you are supposed to hit them on certain areas, but some of them don't give you a visual or audio cue that you are doing damage, so I have to keep checking the life bar to see if is doing anything
-Some levels have walls of the side, enemies can pass-through them but you can't, so is impossible to hit them without taking damage yourself
-Some levels have pillars that appear at random. It already happened multiple times, than when a boss enters, and you lose control of the character for a few seconds, but there is still a pillar coming, so you get hit without being able to avoid it
-I encountered a few audio glitches. Like after losing a run, it takes you to the menu, game may still play some of the audio in the background.

Neutral:

-It takes just a bit to get used to the 3D perspective

Never played a lot of Space Harrier. That being said, I really enjoyed my time playing this. Spent over 6 hours and got all the achievements. This is a really fun and addicting game! It left me wanting more, honestly. Asura is tough, cool, cute, robot waifu that I would like to see more of. I know this is this indie dev's first game, but I would love a sequel/spin-off to Asura. I can definitely see the potential. Especially, with all the side characters shown. Eh a man can dream. Anyways, as a man who likes cute anime girls and fun gameplay, this is a big recommend for me. Looking forward to seeing what this dev has in store for the future.

this is what game should be. simple. fun, engaging.