Reshiram

After 236 Soft Resets Reshiram came shiny

You can find Reshiram in the Flabed Cave (You need a level 100 Pokémon in your team)

Level 50

Nature: Lax (+ Defense - Sp.Defense)

Ability: Turboblaze (Moves can be used on the target regardless of its abilities)

Moves:

Dragon Breath (Dragon)

Slash (Normal)

Extrasensory (Psychic)

Fusion Flare (Fire)

Next Shiny: Giratina

Poochyena

After 222 meetings Poochyena came shiny

You can find Poochyena in Routes 101, 102 and 103 using the Dexnav

Level 4

Nature: Bashful (Neutral)

Ability: Quick Feet (Boosts the Speed stat if the Pokémon has a status condition)

Moves:

Snatch (Dark)

Howl (Normal) 

Next Shiny: Reshiram

Next Shiny

This afternoon i will upload my shiny Poochyena

Eevee

After 657 meetings Eevee came shiny

You can find Eevee in Route 116 using the DexNav

Level 21

Nature: Bold (+ Defense -Attack)

Ability: Run Away (Enables a sure getaway from wild Pokemon)

Moves:

Charm (Fairy)

Quick Attack (Normal)

Bite (Dark)

Refresh (Normal)

Next Shiny: Poochyena

Phantump

Phantump its graceful to see it shiny

You can find Phantump in Petalburg Woods with the DexNav

Level 6

Nature: Serious (Neutral)

Ability: Frisk (The Pokemon can check an opposing Pokemon's held item)

Moves:

Venom Drench (Poison)

Confuse Ray (Psychic)

Astonish (Ghost)

Next Shiny Tomorrow: Eevee

Dewgong

Dewgong its difficult to see if its shiny or not

This Dewgong was my first Dewgong in Omega Ruby

I didn't know it was shiny, but when I captured him i saw the red star of shiny.

You can find Dewgong in the Shoal Cave with the DexNav

Level 34

Nature: Sassy (+ Sp.Defense - Speed)

Ability: Thick Fat (Boosts resistance to Fire and Ice type moves)

Moves:

Sheer Cold (Ice)

Aurora Beam (Ice)

Aqua Jet (Water)

Brine (Water)

Next Shiny: Phantump

Swadloon

You can't find Swadloon in Omega Ruby, but if you have a Shiny Sewaddle you can evolve it.

Sewaddle evolve into Swadloon at level 20
Swadloon evolve into a Leavanny when leveled up with frienship

This is my Sewaddle evolved into a Swadloon

Level 25

Nature: Timid (+ Speed - Attack)

Ability: Leaf Guard (Prevents status conditions in sunny weather)

Object: Mental Herb (Removes the effects of infatuation, taunt, encore, torment, disabled and cursed body)

Moves:

Agility (Psychic)

Protect (Normal)

Bug Bite (Bug)

Razor Leaf (Grass)

Next Shiny Tomorrow: Dewgong