Firstly of all, Popeye is a terrible, terrible movie.
Secondly
It got a little better as you entered the post-game in which you got a new character which can use all the upgrades at the same time. In the main game you can only have a longer range bullet shot, longer horizontal hover, OR a high vertical jump upgrade active at a time. Because of this all the levels are designed so you can complete them without any of the upgrades, hence the sense of zero progression as you play the main game. Once you get that character which can use all 3 (but not until you have completely beat the main game and gotten all the collectibles) you can play what are basically challenge rooms hidden within the levels. Those areas are designed to require the use of all 3 powers in order to progress.
It would have been preferred if the challenge rooms just unlocked in Granny's Attic instead of requiring you to play through parts of the levels again. In the end you have to play through all the levels at least 4 times to get the 100%.
At least 1 time to collect all 100 diamonds in each level and reach the end of the level
Another time as the main character to find and complete his 20 challenge rooms
A third time as granny with the 3 upgrades to complete the 20 granny challenge rooms
A fourth time in a spooky level variant of the main levels in which you can't kill the enemies (most of the time) because they are replaced with ghosts and some of the terrain is slightly different and you have to recollect the 100 diamonds in each level.
The jetpack controls are a little weird, but I got used to them fairly quickly. Whenever you tap the hover button you stop your descent and can move horizontally until you run out of fuel and have to touch ground to recharge. One of the upgrades gives you a vertical rocket jump which is triggered by UP + jump, but it didn't appear to fire correctly 100% of the time. It only seems to fire right if you have the stick directly in the up position. That isn't much of an issue when you are on solid ground and can line up the jump, but in many of the challenge rooms you are moving horizontally just above deadly spikes. If it doesn't register your vertical thrust command then it shuts off your jetpack instead (as pressing just jump while hovering is the command to stop hovering) and you are killed on the spikes.
I also had troubles with certain pads that trigger when you press the jump button. Often times I would need to use the jump feature when on those pads, but instead of jumping it triggers their effect which greatly messed me up on several occasions.
Also it didn't happen often, but a few times the game called for you to rocket jump up into an area where the enemy is patrolling in the air, and you can't see them from down below. You can only launch and hope that they aren't in your path at the top of your jump. In that instance whether you take damage (3 hits kills you) is completely luck based.