Ol' Tarzanvania here was clearly shooting to fill the Castlevania-shaped hole in the Turbo lineup, and it actually does a pretty competent job. It's not quite as sophisticated as the best of your melee-weapon-based Badass Platformers like the aforementioned Belmont adventures or the NES Ninja Gaiden games, but it manages to hit most of the right notes.
The setup is pretty basic -- Axe-Crazy Tarzan has to axe his way through a cult of bald gremlins and trained bears 'cause they took his girlie Flare as a sacrifice to their dark god or somesuch. It's old-school in composition and definitely on the challenging side, you get three lives only with which to do this and 1-Ups are very few and far between, but you do get to continue from the current stage three times before it's back to level 1 with you.
It's important to have a little historical context when evaluating this one. In both Japan and North America, it came out just before the Sega Genesis did, back in that brief window in 1988 / 1989 respectively where the Turbografx was the first "16-bit" (kinda) system to the market and was only competing with the NES. So colorful graphics and big sprites were the order of the day, to really try to play up the difference between the two -- see also China Warrior, Keith Courage, etc. Often, this came at the expense of gameplay, which was why Legendary Axe's relative solidness in that department was such a pleasant surprise and endeared it to early Turbo adopters desperate for something that was actually fun to play.
Levels tend to be on the small side, but do have something of a non-linear aspect. Right off the bat, you can shimmy down a vine into a pit for a totally optional battle with a giant spider, which nets you an axe power upgrade and some bonus points if you go for it. Later levels reward exploration similarly with 1-Ups and points, and there's no timer over your head forcing you along.
Though it would be verboten to show off your final boss prior to release these days, back in 1988 Victor proudly had screenshots of their massive end boss, Jago, plastered all over game magazines. The idea was to incentivize you to actually see this big monster in motion, which seemed to work well for sales, and also turned out to be fairly impressive for the time.
I only have two major complaints with the game, but they're significant enough to cost it points. The first is that jumping from vine to vine, which you're often tasked to do over insta-death pits, can just go get fucked. It's like the level designer just finished playing Jungle Hunt/King and was like "how can I make this mechanic more arbitrary and maddening?" The other might be an emulation or modern control issue, but Axe Tarzan seems to be a little slow on the uptake when told to duck. All the other controls are perfectly responsive, which makes me think it's an issue in the game's code.
Those issues are reduced somewhat for modern gamers as you'll likely be playing this on a platform with save states. Even with some amount of frustrating control responsiveness, Legendary Axe is still worth a spin for fans of the pre-Metroidvania Castlevania games due to the inventive enemy designs and kickin' chiptunes soundtrack.