>Dizzying and woozying, it's a psychic confusion
Psychic is both the power of mind and the ability to control other's minds by warping their thoughts. This also leads me to believe stuff such as a psychic field or a trick room is a field where beings inside it have their minds warped, at the extent of believing they're slower than they really are.
>Normal is ordinary, yet simple is best
If you can't classify it or it's basic in nature, then it's Normal.
>Swimming smoothly with splashing grace
Almost every Water type also lives in water. The few exceptions are where it's thematically fit, such as geothermal energy (Volcanion) or pearls found underwater (Palkia).
>Grass and flowers thrive under the sun
This one's obvious.
>Drawing power at its source on the ground
>Let's soar freely upon the blue sky
Except for Doduo, Dodrio and Gyarados, all Flying types can fly.
>The buzzing of insects is bugging us out
Bug types are insects and related species such as arachnids.
>Rugged rocks, rumbling rocks, attack with guts
Anything dealing with not just rocks but also being able to resist a lot. Or being prehistoric.
>The sly villain is cackling darkly with an eeheehee
Dark is not "dark", but evil. It's all evil Pokémon or Pokémon who bring misfortune, or also mischievous Pokémon.
>The body of steel shimmers and shines
Shining metal bodies or Pokémon related to stars, which are made out of metals. This still doesn't explain Lucario, but I gotta guess its bones are steely, or maybe its hair.
>The strong dragon roars out with its mighty jaws
Dragons are the roary reptiley type. Or Pokémon that follow a dragon related pun, so long as it makes sense in Japanese (ryuu) such as Mega Ampharos (Denryuu) or Tyrantrum (both roary reptiley and dinosaur means kyoryu in Japanese).
>The fairy charmingly and gorgeously strikes it out
Except for the tapus it's literally the cute gorgeous type. Get rekt dragonfags.