This feels like a story with a lot of potential to grow. I enjoy the art style and the animation looks very fluid, never stiff or inhuman. The music adds a lot, without ever being distracting, which I appreciate.
I think that if you keep working on this as a series, people (including me) are really going to enjoy it.

This is beautiful, and I would love to see it as a feature length film. Bravo, truly.

You've gotten a lot of good criticism and most of the stuff I was going to talk about has already been said.
I feel like this game has a lot of potential and parts of it are genuinely fun to play. However, issues with the game's "feel" are what drag it down.
The fact that the character slides a little bit before stopping is incredibly frustrating during precise platforming. It wouldn't be so bad, but the level design mandates perfectly timed jumps onto 1 tile wide platforms, and it's nothing but frustrating to try to do that when you slide off the edge every time.
I like the mechanic where you catch on ledges, but I might consider making it automatic. I got used to having to press a button to grab the edge, but it's kind of a convention for that to happen automatically regardless of player input.
The hook is really difficult to use and requires near perfect timing. Irritating, but maybe that's what you were going for.
I might just be missing the tutorial statue that tells you how the upwards blowing wind works, but it took me forever to figure out that you had to hold jump to keep floating upwards. I lost nearly twenty lives just trying to get through those jumps.
I get it if you're looking to make a challenging game, and I respect that. I enjoy games that offer up a player a more "hardcore" difficulty level. However, if a game is difficult because the controls get in the way, that's just infuriating to the player and not remotely fun.
All this being said, I can tell there's been a lot of work, time, and polish put into this game. It really does seem like a worthwhile project, and I think that with a few tweaks it could be an incredible game. Great pixel art, great music and sound design, even great level design to boot. Just a few control fixes and things here and there can vastly improve this game.
(Also, I disagree with some of my fellow commenters, I kinda like that the axe takes some time to swing. It feels heavy and satisfying to use, and it force me to actually think about what I'm going to do in advance. I think it would be even better if it were possible to hold down the button to hold your attack, and have it swing on release)

A pretty fun little platformer with cute art and pretty solid programming. One little nitpick I have is the way the lizard controls on the ground; he seems to speed up the longer you hold down the key, which for this game isn't a choice I like since it leads to either a) the player not being able to move quickly right off the bat or b) the player ending up moving way too fast when they're trying to stick a tricky landing after flying from some distance away. This could be fixed by having a run key, or by just making it so that the player has the same movement speed at all times.
Sound and music would add a lot to this game. But overall it's fun enough that I played it all the way through, and with a few minor tweaks and some more level sets it could be something really great.
P.S.
If you're looking for someone to help you out with music, just PM me.

Hey, would you look at that, chance has it that I'm reviewing one of your tracks again. Let's do it.

Right off the bat, I can tell this will be a piece with a good sense of atmosphere. I really like whatever the sample with a ton of reverb is.
0:04-0:24 I love how skillfully you manage multiple different instruments, lines, and textures simultaneously, without any one becoming more "important".
The moment leading into 0:24 is a very clear signifier of a new idea, but it also manages to be quite subtle. Well done. Also, I love the lead you use at 0:24, it's a very cool sound.
The way that the arpeggiated chords and the melody interact is really beautiful. The texture of the piece is never boring or one note.
0:48 I'm digging the pad sweeps you used here.
1:00 Is that a tempo change I just heard? Nice and subtle.
1:07 The clap-like sound you used here works really well.
1:18 The build-up at 1:18 is pretty good, but it feels just a tiny bit typical, what with the noise sweep and the basic edm snare at 1:15. Perhaps it could be a little better matched with the rest of the song (really minor nitpick, I'm just trying to find something useful to point out so I'm not just gushing the whole time haha).
1:19 I really love the compound meter feel here. The lead is right in the sweet spot of not being too grating, but also managing to stand out and convey the melody over the rest of the song.
1:37 The chord change here is unexpected, but that's something I tend to really like, so kudos to you on that. I would try to get all smart and describe it with music theory, but my keyboard's still at a performance space.
1:43 Another really nice transition. Well done.
1:50 I always love to hear the dorian mode. I really like this section and I wish you would've spent a little more time exploring it. But that's not really a criticism, I respect your choice as an artist here. Also, I'm typically not that crazy about the type of midi piano sample you used here, but you totally made it work within the context, so good job!
1:56 Nice chromaticism.
2:00 In a song full of nice transitions, this moment is a little jarring and unexpected.
2:05 I like the energy in this section, but it's all coming across as a little much. My ear isn't really sure what it's supposed to be listening for. What I do like about this section is that it's in an odd time signature (5/4 I think), which is a cool choice that not many producers would have the gall to make.
2:24 Good transition around this spot. Also, I'm a fan of the groove you shifted into here.
2:30-2:35 I like this idea, but it's kind of short lived. I would say it's a satisfying conclusion to the section proceeding it, but that's immediately upended by 2:36.
It's an odd choice. Very out there. The following section builds up a lot of tension. My ear doesn't really say "Hell yeah!", but it's an interesting idea and one I would say a lot of people wouldn't think to explore.
2:57 Another (albeit slightly less) jarring transition. Again, it's not super pleasing, but music (and art) isn't always supposed to please. I will say though that this section doesn't really fit into the rest of the song very well at all. I understand that the point of this song was experimenting with a bunch of contrasting ideas, but up until this point everything kind of made sense together, even if it was all very different. This section kind of throws a monkey into the wrench works (I think I got that one right, haha).
3:18 This transition is alright, and I like the idea that it segues into. You did a fantastic job using samples and different textures to create atmosphere here.
3:42 I like the idea of a return to your original idea, but I don't feel like it was set up all that well.
3:51 Interesting chord progression here. I like it.
Transition around 4:00 is quite well done.
4:20 The setup was good, but the actual transition itself left me surprised again, and not in a good way.
4:46 I think I mentioned this in the other review, but I like how you take ideas we've heard before and spice them up a bit when you revisit them later. It's a good habit/practice to get into, really helps set you apart from copy paste DJs creating monotonous music.
Around 4:56 to the end is just gorgeous. I love the effects you used on the piano samples. The tempo change feels meaningful and adds a lot to the emotion of this section.

I hope I wasn't too harsh with a few of those critiques. For the most part, this is a really nice piece that showcases your skills very well. There are a few areas that could possibly use improvement, but most of it is interpretation stuff, which can get kind of subjective. All in all, this is a work that you should be proud of.
Happy writing,
MaverickMode.
P.S.
This type of episodic piece could be called a rhapsody.

These artworks are amazing. Truly blows me away.