Sonic Adventure DX Director's Cut Tips

All Power Ups I know so far.
Light Speed shoes: Allows you to do the light speed dash. In sewer near city hall, can't miss it because you need it to go to Casinopolis.
Crystal Ring: Less charge time for light speed dash. In hotel elevator, you need light speed shoes. Can get after Light Speed Shoes.
Ancient Light: Allows you to attack enemys with the light speed dash. On the rock near the bridge to the Master Emerald shrine, need it to enter Red Mountain.

Rhythm Badge: Allows You to do the continuous tail attacks. Get in past. Needed to get out of past. To the right after the stairs on the other side of the building.
Jet Anklet: Allows you to fly faster. Can get in begginning of game, in the sewer near Twinkle Park.

Shovel Claws: Allow you to dig. It's in the room where the monkey in the cage is in. Needed to go to Red Mountain.
Fighting Gloves: Allows you to do the Mega Heat Knuckles whatever Attack.
Can get on your first time in the Mystic Ruins Jungle. Go on the tree near Big's house and go on the wall, find a floor and go straight.

Warrior's Feather: Allows you to do the Spin Hammer Attack. Can get by tieing with or beating Eggman's score. Get by playing Hedgehog Hammer when trying to escape.
Long Hammer: Play Hedgehog Hammer on the Egg Carrier for a second time on the second visit before you beat Final Egg or Post-story mode. Try to beat your High Score. Increases the length of the Spin Hammer Attack.

Life Belt: Allows you to swim in water. Near the pond near Ice Cap's ladder.
Power Rod: Allows longer fishing distance. You got to be an idiot if you didn't see the power up under big's bed in his first cut scene.
Lure power ups: there are two so far. One in the sewer near twinkle park (under the hole you go through to get Tails's jet anklet) and the other on the Egg Carrier in the Prison Room (you can find it easily, you can't miss it). Allows you to catch bigger fish.

E-102 Gamma:
Jet Booster: In the room that says do not enter when your Sonic or Tails. There are two so if you go to the room with water in it, just go to the other one on the other side. Need it to fight Sonic on the bridge. Allows you to hover till you hit land or till you fall.
Laser Blaster: Allows you to hit targets in wider range. It is not like the SA2B laser blasters, well, kinda. In the room with the water in it on first visit, if you found the booster without going to the room with the water, it's in the opposite room. It's filled with water on first visit but not on second visit, you can get it before hot shelter, after E-105 Zeta (not Epsilon who is E-104), or after E-101 mk II Beta upgraded.