God I miss levels like this.

Finally I have some time to spend playing other people's levels and criticizing them to death!

It's not a bad level. It has a few interesting challenges/puzzles and the plot is funny (and you didn't abuse trap/enemy objects, like many people do on their first levels ), but there are quite a few problems. The main issue is that, just as theiza said, the level lacks polish. There are several paths that you obviously didn't mean for the player to take, but they are reachable and lead to void screens/wall swims. Here you have a list of what I found:

Spoiler: Void screens / Wall swims (click to show/hide)

x1001y999: You can just jump/climb the wall to the left and go above the keylocks. Then you can just jump to the left side of the screen and immediately win the level   Also, if you jump to the right of said screen, you get stuck on the left wall in x1002x999 (entrance to "chess land"). You can also double-jump from the top of the pillars and reach a void screen.

x1000y1004: If you jump straight down when you collect the umbrella power-up, you'll fall into an endless void pit.

x1003y1003: The wall is climbable once the enemies have fallen onto the floor, and it leads to another void screen.

x1005y998: You can reach a void screen if you double-jump to the left from here.

x1003y1000: This is the area where you collect the eyeball. If you try to climb up the left wall, Juni gets stuck into a wall-swim. If you want the players to use the teleport spot to the right, you should make the left wall unclimbable (not necessarily using the "no-climb" object)

Aside from this, here are a few suggestions for improving your level:

x1002y1002: If you put so many "Sign" objects, the text will start moving with you as you run through the screen. You should put only one "Sign" object and then fill the rest of the text area with "Sign area" objects.

x1011y1004: This is just a minor glitch, but the woman should have been placed on the floor. If you put her over that block, she'll start walking in the air

x999y1003: Instead of using so many shifts here, you could just put a Warp object (obj. #20 on bank 0) on x1000y1003 and then specify a "warp left" destination for that screen. This way, you can warp Juni to wherever you want as soon as she tries to go left on that screen.

x1001y1002: There's a visible shift spot floating in the air on this screen... but it looks like it doesn't have any purpose whatsoever.

I also agree with theiza on the starting power-ups. It would have been better if the player didn't have access to some of these powers until much later. Having the climb and high/double jump power-ups from the start makes most of the challenges too easy.

As for the level design... well, I'm not really the best person to give you advice on that, but I thought that some of the level's areas felt too empty and bland for a challenge level, specially the "white castle". Maybe you could add a few platforming challenges or make the castle more maze-like, adding multiple paths. You should also try to fill up those screens adding a ceiling and a more detailed background, instead of just using a plain green gradient.

Anyways, congrats on finishing your first level   I hope you find all this rambling useful and I apologize if I sounded too harsh.