Best Level Ever: The Battle of Hoth had already gotten a decent rendition in Super Empire Strikes Back, but this game just took it to the next level. The last mission, the Skyhook Battle is a close runner-up for this title. Hoth was such a well-received level that they spawned a whole other series.
Heartwarming in Hindsight: When Guri is defeated by Luke, he spares her and asks her to come with them in order to reprogram her. She rejected the offer, responding that she'll die if they will try. Later, Guri decided to, and her effort was successful. Well done, Luke!
Nightmare Fuel: The sewers. It's entirely possible to be instantly killed by dianogas in an early stretch before fighting them on a regular basis. The level is hell for people with a fear of underwater creatures.
And the music. The dark, dank sewers were scary enough without it.
Polished Port: Arguably, the PC port of the game is a significant improvement over the N64 original, what with much more responsive controls and fully voiced, rendered cutscenes that hold up well enough till this day… that is if you're using a system this game was made for, as newer ones sure cause a few problems.
Schizophrenic Difficulty: The walking stages of the game are much harder and take way longer to get through than those that have you drive a vehicle (save, maybe, for the swoop race which, while tough, is still relatively short so you don't have to worry too much about losing your progress in case you run out of lives). The third level, taking place in the Asteroid Field, for instance, is ridiculously easy in particular and can be beat within less than two minutes.
George Lucas himself said that it qualifies as a piece of Star Wars media that should have been an official film. Given that Disney has declared all EU material non-canon, the Outrider's cameo in A New Hope: Special Edition probably brings Shadows the closest to that status it can possibly get.
Squick: Guri is fully equipped as a human replica droid. And Xizor has actually used said equipment.
That One Boss: Rather fittingly, Boba Fett. He has his trademark jetpack, the same kind of homing Seeker missiles you've been using since Hoth, and a close-range flamethrower that will kill you quicker than you can blink, even if you're at full health. He gets even worse during the second stage of the fight when he takes you on in the Slave I, and all of this comes at the end of a definite Marathon Level.
Although neither he nor Slave I will follow you outside the launchpad, where you can find extra powerups. When dealing with Slave I in particular, you can just hop between the gaps on your jetpack, fire a few shots at Slave I, then dip back down before it can fire on you. Lather, Rinse, Repeat.
The Gladiator from Xizor's Palace has three "forms": the full figure, its torso (with a rocket booster to propel itself around), and its head. When its second form appears, a labyrinth forms that also has some enemies inside. When the head is left, your jetpack malfunctions. And it always spams the laser (with a really big area span) no matter where you are.
Ord Mantell junkyard. You have to jump from train car to train car, and from train to train- all with physics that will send you helplessly falling to instant death if you attempt a jump at the wrong time. You will fall a lot before you get familiar enough with the mechanics to beat the level; and at the end of it is IG-88.
The widely reviled Swoop Bike chase level; a level that forces you to drive at breakneck speeds through cluttered streets and levels, with countless opportunities to get stuck, slow down, and crash and burn. The only thing that salvages the level is the enemies actually slow down so you can attack them.