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Ruins. In water. Kinda like Sonic 1 but with more machines and pipes. We shouldn't have to explain Sonic water mechanics at this point but in case you don't know: move slower in water, drown unless you pick up water bubbles or resurface, platforming even more annoying.
Time travel dick moves really start in this area! You still get a few places where you can easily go back and forth between springs, but other places require more planning, jumping or maneuvering around enemies to travel through time. The video's first jump to the past shows this in a long stretch with dragonfly bots above. It doesn't seem hard, but one fall or bad jump will ruin that warp forever.
- Past: Orange mountains in the background and a weird green tint to the level as well. A bit... clowny? Some machinery, early plant life, fish.
- Bad Future: I hope you like pink! Seriously though, there's a great aesthetic here - rust, trash blocks, broken pipes. Pretty cool.
- Good Future: An aquarium or vivarium. Lots of shiny surfaces and machinery.
BADNIKS
Tonbo (dragonfly)
Flies back and forth. That's literally all it does. 
Flies slower in its damaged form. Not listed in the manual.
Taga-taga (that crustacean thing again)
It's back from Palmtree Panic! This time, it swims in a straight line towards the right. When Sonic gets close, it fires three spikes from its back then dashes away. It has a damaged form this time, which is just helpless.
Amenbo (water strider)
Glides along the surface of the water and fires flashing projectile... unless it's damaged, in which case it goes slower, doesn't fire and just looks sad. We didn't see much of these. Not listed in the manual.
Yago (crayfish)
Swims around the bottom of the water slowly, then lunges towards Sonic when he approaches. The damaged ones are much worse at this but they look really cool: their rear metal housing is gone and they have this sickly color. Not listed in the manual.
BOSS: Eggmobile, in the water
Phase 1: You're in a maze, chasing Eggman. Follow him and hit him four times, at which point he will escape to a large underground room. While he's escaping, he will go fast enough to always be ahead of Sonic. You can't leave the maze until he's been damaged enough!
Phase 2: Eggman will surround himself with air bubbles. These are Eggman's only shield as well as Sonic's only air source here. The Eggmobile periodically swoops down and towards the other side of the screen, firing four shots from its underside while doing so. Once it reaches the other side, it rearranges the air bubbles to fill in any gaps from the ones that Sonic breathed in.
Like the video said, this is mostly psychological; Eggman only needs one hit to die in Phase 2 but you'll have few to no air bubbles left when he's vulnerable and he will keep shooting at you. If you can get in front of him or get invicibility frames from getting hit, he's a piece of cake.