Achievements

Achievements are optional challenges of varying difficulty in the Pokedex that ask you to do tasks in exchange for rewards. In order to get rewards for any Achievements you must obtain the Pokedex from the Mt. Moon Challenge Level. Afterwards, any Achievements you have completed will show that they have. Claim your rewards/check status of your completion via the Pokedex.

Shiny Hunter 1
Find the following wild pokemon: shiny Rattata, shiny Pidgey, shiny Geodude and shiny Zubat.

Reward: Shiny Onix

Tips

 * A good place to look for the Pokemon is Mt. Moon 1, as it has Rattata, Geodude, and Zubat.
 * You must "activate" the achievement first to see the Pokemon or they won't count.
 * You don't have to catch the Pokemon for it to be recorded in the achievement section. You only need to see it in the wild.
 * Why don't you try Vermillion Gym, it has all four of them.
 * for Rattata, try Route 2, there come a lot...

Star wars
Defeat a Starmie in the Cerulean Gym 1 level .

Reward: Shiny Staryu

Tips

 * Have one Pokemon that knows an attack to turn Starmie around so it does not escape. Attacks that can turn Pokemon around are Whirlwind, Roar, Growl, and Confusion.
 * Have an electric type (Pikachu or Raichu) who can use Thunderbolt or Thunder and a Victreebel with Leaf Storm, Solar Beam or Giga Drain
 * Starmies spawn on the right path, so having a Parasect with Spore (100% sleep rate) on the right-bottom panel will assure that Starmie is put to sleep.
 * Another easy way that you can earn this is to use a pokemon that knows Double Slap on the top-right panel, a pokemon that knows Magnitude in the middle, and a pokemon that knows Whirlwind, Roar, Growl, Drago Tail or Confusion to make it turn back on the right-bottom panel. Double Slap can take out some flying types, Magnitude can take out the rest and deals a considerable amount of damage to Starmie, and Whirlwind, Roar, Growl, Dragon Tail and Confusion to make sure it does not escape.
 * You can also try a pokemon that knows Fissure, Horn Drill or Guillotine. Be sure that the pokemons level are higher that the Starmie.

No Advantage
Defeat the Cerulean Gym 1 level without using Electric or Grass type Pokemon.

Reward: Shiny Tentacool

Tips

 * Since the conditions state you can't use Electric or Grass type Pokemon you could use Pokemon with Electric or Grass type attacks.
 * Try a charizard or pigeot using wing attack and put it in the center and put level 30 golems using rock blast in the other spots

Win without wind
Defeat the Vermillion Gym Challenge level without the move Whirlwind.

Reward: Entei Avatar Hat

Tips

 * You can use a Pokemon that knows Roar, Growl, Dragon Tail or Confusion as it has the same effect.
 * It is bugged in v3.4. To get it, you should leave only one candy.

Needs More Candy
Defeat the Vermillion Gym Challenge level with more than 1 candy left.

Reward: Suicune Avatar Hat

Tips

 * Let the first Pokemon from the first 2 waves reach the candy. Place 2 pokemon who know whirlwind or roar in one of the four places close to the candy (1 either side, top/bottom doesn't matter) when the first Pokemon from either side reach the candy. Then, place 1 attacking Pokemon in each of the four corners. The whirlwind/roar will keep 2 candy holding Geodudes in the center whilst you knock out the other Pokemon. When all others are defeated defeat the two Geodudes that you kept trapped. note: this actually isn't avaiable
 * Use four Golems/Gravelers with bulldoze on the four corners closest to the candies. Then use two pokemon that knows physic on the middle right and middle left to attack the pokemon from the for corners. Make sure your pokemon are at least level 44 or above or the Raichus will go past.
 * Or, you can try to level up your pokemon untilit works. As the pokemons from this challend don't attack, explore pokemons with strong attacks, as Victreebel, Flareon, Gyarados, Raichu, Dragonite and Machamp.