This is a fun little platformer with some side scrolling flying, all for a quest to craft cheese! I managed to get all the way to Chapter 5 (haven't beaten it yet), and have been enjoying the retro art style. The music certainly was catchy, and the sounds fit the aesthetic you were going for.
But I have a few issues, since this game got me to rage quit on the last chapter (the fact that there wasn't a in game way to quit didn't help me). Mainly my anger was towards wanting to complete it, but the level felt at odds with me. Mostly the RNG of the falling barrels, in that the falling barrels ARE RNG based. I felt that there were too few openings to get across ledges, which the shortness of the time stopper doesn't help with trying to time the few times a good spacing in the barrels worked. I'd also like to note my anger probably arose from Chapter 4 with Chapter 5 being my breaking point. Chapter 4 felt unfair mostly since everything damaged me (trees, birds, ground, gun fire), it makes sense for these to damage me but having times that I would get trapped by birds overhead and an upcoming tree ment I would lose health anyways. I did beat the farmer once before my victory, but the tree killed me (XP).
So I have a few thoughts on favoring the player while keeping a seemingless fascaude of RNG being applied. For Chapter 4 a simple fix would be to keep birds (and fuel since I had fuel spawned in trees before) generated just high enough the tree line so the player could "thread the needle" when caught between them. The tree line meaning whatever tree you have on screen would set the boundary for how low the birds can spawn. It's still pretty difficult, but during my play through once I decided to go at it calmly and wait for the opportunities it became possible. I do really like that you added that the trees become more frequent the longer the level is, just to give the player the availability to speed up the fight.
I'd also like to quickly mention that the hitboxes could be improved. I've heard that (depending on the game, but it seems to apply to this game's style) damaging hitboxes should be slightly smaller than they appear, while useful hitboxes should be slightly bigger than they appear. The hitboxes on Chapter 2 feel larger than they are (which is probably because they are a square, I'd assume). You could make a small fix to that by making the boxes half their current size. Or if they are a square, rotate them so they are a diamond (:P).
I now give my suggestions for Chapter 5, quite a few in fact. These are more "choose one to see how nicely it works" suggestions, though a combination would also work.
1) Since this is a vertical level, adjust the camera so the player is closer to the bottom so they can read the barrels that are coming up. This gives the player information that helps them make these difficult decisions of timing and jumping. I recommend this adjustment the most as it would be simple and makes the player feel like the game is a bit more fair.
2) If the player is on a certain side of the map, have the barrels occasionally spawn in a semi-random pattern that favors the player. As in the barrels could spawn in a pattern that looks like "steps" to the next ledge. Most commonly the barrels spawn one after the other which sometimes makes "walls" that prevent the player from passing if they didn't time it right.
3) Mentioning the "walls" of barrels, another suggestion would be to space them out a little more. In Chapter 2 the left side after the timer block (that also disappears if the player is to close to the right of it) requires a jump with a block right above it. Attempting this jump a few times made it clear to me that it would be difficult (not impossible, but not viable if I want to prevent falling) to jump from those gaps. The "walls" of barrels would have these kinds of gaps. Consistently executing a jump feels better than executing a tricky one every so often.
4) It is interesting that the platforms are from side to side, but more platforms could help. Heck, it would also make the boss fight a little more interesting if rocks were sometimes thrown in besides barrels, since you have the rocks programmed to break and not injure the player.
5) I did see what the space pirate looks like, but I fell before reaching them (I got as far as underneath them). I'm not sure how many hits they take (hopefully 1) but I think it would make for a more interesting fight if it was a 3-hit progression. Have the pirate on the second ledge and as the player hits them, they progress to the next higher ledge until defeated.
6) This doesn't feel too much like a boss fight to be honest, so a rework to convey that the space pirate is attacking your ship would make Chapter 5 end on a better note. Perhaps have the barrels being an attack phase and you need to use the time stopper to squeeze between a tight fit. You could also incorporate the laser again, this time having it sideways and using the time stopper to pass it. The fight could be a simple attack phase and vulnerable phase.
7) Since is could be difficult for some players (like me) to reach them all the way up there, you could add an option that triggers for when the player dies X times, provide a prompt to make the level easier. Some folks (like me) do not have enough time to play and beat games, despite our desire to do so. This allows all kinds of folks to complete the game, even though your intent would be for the more difficult (intended) way to fight the boss. To give players a level of accomplishment, you could add a "certificate of competion" to those who take the intended difficulty.
Thank you for your time and effort, this is a neat game but it could be revised a little. Still pretty impressive for making it under 10 days. Astronomical work!