The first one was so awesome, it made it into I Wanna Be the Guy as the theme for the Final Tower of the Guy, continuing on for The Guy's first form!
Breather Boss: King Bee is considered MUCH easier than the previous two bosses and the following boss.
Demonic Spiders: Many enemies can be this, but the Tyrannosaurus and Allosaurus are the worst of the bunch, being able to cause massive damage very quickly, and also being nearly unbeatable if you're not tall enough.
Game Breaker: Boss fights become much easier once the player discovers that undergoing an evolutionary change also has the beneficial side-effect of also healing all your health. Just stock up on EVO points prior to the battle, and when you're getting your ass kicked, just go to your evolution menu and make one small change (like adding a horn), and you'll be back in business.
Also, Cro-Maine. After he tells you his story (namely, how he was bullied by the Monkey-Humans), he suddenly changes from a calm demeanor◊ to being extremely pissed off◊. This forum even mentions that he has emotional issues. If so... just how severely the Monkey-Humans abused him if he is so violent and moody?
Goddamned Bats: Trilobites in the Fish Age chapter, most flying enemies if you're not a bird, and the monkeys and dino-people in the final chapter.
It Was His Sled: The Final Boss is a monstrous cell with an awesome battle theme. Thanks to I Wanna Be The Guy, this song is the first thing related to the game some newer players learn.
Nightmare Fuel: Bolbox can be this sometimes. The level with the cockroaches borders on it as well. As for the Queen Bee's face... ouch.
Older Than They Think: The SNES game itself is HEAVILY based on a much older game by Enix called 46 Okunen Monogatari: The Shinka Ron ("4.6 Billion Year Story: The Theory of Evolution"), released only in Japan in 1990 on a very obscure home computer called the PC-9801.
Signature Scene: The final battle with Bolbox. Mainly because of how bizarre the entire scenario is, the awesome music, and the brutal difficulty. In fact, thanks to I Wanna Be the Guy, this might be the first part of the game one learns about.
Mt. Brave is partly this trope and Brutal Bonus Level (it's optional). Birds pick you up and force you to start over. And the reward you get... is becoming a new class of evolutions, forcing you to start over. Unless you figure out how the Cloud Maze and River of Asteroids work, which give you the REAL reward: The Dragon and Gargoyle forms, along with a ton of Evo Points.
The Woobie: Yeti Avenger and Cro-Maine. The former one is the descendant of the Yetis you killed (humiliating the Yeti race in the process), while the latter one was a victim of abuse and bullying by his own kinsmen, the Monkey-Humans, because he had less hair and was smarter than the rest.