Awesome Music: The main theme song, "Override the System".
Demonic Spiders: Black Monitor Men. For starters, their attacks are the hardest to dodge, and downright impossible to parry.
Armored Cones. There are a few of them in the game, and their weakpoint is pretty obvious, but they have a high hitpoint/guard meter, and can summon tornadoes that actively chase you down.
Goddamned Bats: Cleaner Dogs, Standroids, and pretty much all flying enemies are very much this. Not difficult to eliminate (especially if you use business cards or the Galaxlayer), but annoying to catch up.
That One Boss: The backlot elevator fight against Kazama in Asaru's story is this. Not only does he jump around the level either shooting or throwing bombs at you, he also has the ability to summon gusts of wind. And once you inflict enough damage, the game spawns a few Monitor Men and flying robots that ignore him, culminating with (depending on the difficulty) an Armored Cone.