Now that you've beaten the game, you can do the following:

•Battle Alex (Go to their house)
•Find the roaming Latios and Latias (Interact with the tv in your house to trigger it)
•Catch Cresselia (Graveyard Tower)
•Go grab Genesect and its drives (Ironwork Factory)
•Get an egg and Ditto (Go to the lab and talk to the scientists. Have two empty slots in your party!)
•Turn in your tickets to explore new areas
•Have a rematch with the gym leaders to finish up the story

Alex
Beartic - Lv. 55
Sandslash - Lv. 56
Flareon/Jolteon/Vaporeon - Lv. 56
Gardevoir/Gallade - Lv. 58
Pidgeot - Lv. 58
Starter - Lv. 60

Cruise Ship

Items:
Rare Candy (Check trash bin)
Leftovers (Check fridge)
Max Revive (Check bookshelf)
Eviolite (Talk to madame)

Trainers:
Clerk Chaz - Flygon Lv. 50, Gallade Lv. 50, Slaking Lv. 50
Clerk Britney - Tropius Lv. 50, Ninetales Lv. 50, Espeon Lv. 50
Waitress Jan- Ambipom Lv. 50, Vileplume Lv. 50, Kingler Lv. 50
Waiter Lou - Magcargo Lv. 50, Lanturn Lv. 50, Rhyperior Lv. 50

When you're ready to get off the ship, just go to sleep.

Takon

How to get ticket: Deliver the letters and talk to Sam before beating the eighth gym.

Pokémon:
Lv. 50
Dodrio - 25%
Exeggcute - 25%
Kangaskhan - 20%
Tauros - 20%
Farfetch'd - 10%

Items:
TM24
TM30
TM85

The final image of the puzzle should look like this.



Hojot

How to get ticket: Catch a Goldeen, Horsea, and Dratini, then show them to the Fisherman in the shack on Route 652.

Pokémon:
Lv. 50
Unknown - 100%

Items:
TM02
TM36
TM69

Getting Ho-oh requires Surf, while Lugia requires Dive. The final image of the puzzle should look like this.



Nenoh

How to get ticket: Talk to the scientist on Route 654, purify the Makuhita, then show it to her.

Pokémon:
Lv. 50
Zangoose - 25%
Seviper - 25%
Lunatone - 20%
Solrock - 20%
Castform - 10%

Items:
Soul Dew
TM56
TM71
TM92

Getting Kyogre requires Dive. Surrounding Deoxys are meteorites that will change its form. The final image of the puzzle should look like this.



Shinno

How to get ticket: Give 10 Oran Berries, 5 Sitrus Berries, and 2 Enigma Berries to the mom in Thanatos.

Pokémon:
Lv. 50
Tangela - 25%
Mr. Mime - 25%
Lickitung - 20%
Yanma - 20%
Chatot - 10%

Items:
Gracidea (Check flowers)
Adamant Orb (Requires Strength)
Lustrous Orb (Requires Strength)
TM53
TM57
TM91

Heatran requires Strength, while Regigigas requires owning the other Regis. The final image of the puzzle should look like this.



Avonu

How to get ticket: Beat the game.

Pokémon:
Lv. 50
Plusle - 25%
Minun - 25%
Miltank - 20%
Bouffalant - 20%
Spinda - 10%

Items:
Reveal Glass
DNA Splicers (Requires Strength)
TM58
TM63
TM81

Keldeo requires Strength, while Landorus requires owning Thundurus and Tornadus. Examine the rock the Swords of Justice are facing to teach Keldeo Secret Sword. The final image of the puzzle should look like this.



Gym Leader - Flora
Whimsicott - Prankster - Leftovers
•Stun Spore
•U-turn
•Leech Seed
•Giga Drain
Lilligant - Own Tempo - Life Orb
•Quiver Dance
•Giga Drain
•Petal Dance
•Sleep Powder
Roserade - Natural Cure - Life Orb
•Leaf Storm
•Sludge Bomb
•Rest
•Sleep Powder

Note: Every Gym Leaders' Pokémon is Lv. 70.

Gym Leader - Dr. Volkan
Ninetales - Drought - Leftovers
•Flamethrower
•Will-o-wisp
•Solarbeam
•Nasty Plot
Darmanitan - Sheer Force - Life Orb
•Flare Blitiz
•Superpower
•Rock Slide
•Earthquake
Simisear - Gluttony - Salac Berry
•Nasty Plot
•Substitute
•Flamethrower
•Focus Blast
Arcanine - Intimidate - Life Orb
•Flare Blitz
•Extremespeed
•Crunch
•Wild Charge

Gym Leader - Spurge
Qwilfish - Swift Swim - Life Orb
•Rain Dance
•Waterfall
•Poison Jab
•Toxic Spikes
Toxicroak - Dry Skin - Black Sludge
•Poison Jab
•Drain Punch
•Suck Punch
•Protect
Crobat - Inner Focus - Life Orb
•Brave Bird
•U-turn
•Cross Poison
•Super Fang
Nidoking - Poison Point - Life Orb
•Earth Power
•Sludge Wave
•Ice Beam
•Thunderbolt

Gym Leader - Debbie
Vespiquen - Pressure - Leftovers
•Protect
•Defend Order
•Toxic
•Attack Order
Accelgor - Sticky Hold - Life Orb
•Bug Buzz
•Focus Blast
•Giga Drain
•U-turn
Heracross - Guts - Leftovers
•Substitute
•Megahorn
•Close Combat
•Stone Edge
Scizor - Technician - Leftovers
•Swords Dance
•Bullet Punch
•Bug Bite
•Superpower

Gym Leader - Callum
Drifblim - Unburden - Chesto Berry
•Calm Mind
•Shadow Ball
•Acrobatics
•Rest
Togekiss - Serene Grace - Life Orb
•Air Slash
•Aura Sphere
•Roost
•Nasty Plot
Xatu - Magic Bounce - Life Orb
•Night Shade
•Confuse Ray
•Psyshock
•Aerial Ace
Staraptor - Reckless - Sharp Beak
•Brave Bird
•Close Combat
•Roost
•Double Edge

Gym Leader - Gabriela
Hitmontop - Intimidate - Leftovers
•Toxic
•Foresight
•Close Combat
•Stone Edge
Mienshao - Regenerator - Life Orb
•Hi Jump Kick
•Grass Knot
•Rock Slide
•U-turn
Poliwrath - Water Absorb - Leftovers
•Substitute
•Focus Punch
•Waterfall
•Bulk Up
Machamp - No Guard - Leftovers
•Dynamic Punch
•Ice Punch
•Payback
•Bullet Punch
Lucario - Inner Focus - Life Orb
•Swords Dance
•Close Combat
•Extremespeed
•Crunch

Gym Leader - Vanna
Bronzong - Levitate - Light Clay
•Stealth Rock
•Light Screen
•Reflect
•Gyro Ball
Magnezone - Magnet Pull - Air Balloon
•Volt Switch
•Thunderbolt
•Flash Cannon
•Signal Beam
Steelix - Sturdy - Leftovers
•Stealth Rock
•Dragon Tail
•Earthquake
•Gyro Ball
Skarmory - Sturdy - Leftovers
•Taunt
•Whirlwind 
•Steel Wing
•Brave Bird
Aggron - Rock Head - Life Orb
•Head Smash
•Heavy Slam
•Earthquake
•Aqua Tail

Gym Leader - Blake 
Zoroark - Illusion - Life Orb
•Dark Pulse
•Focus Blast
•Flamethrower
•U-turn
Scrafty - Shed Skin - Leftovers
•Bulk Up
•Drain Punch
•Crunch
•Rest
Honchkrow - Moxie - Life Orb
•Sucker Punch
•Brave Bird
•Superpower
•Roost
Weavile - Pressure - Life Orb
•Pursuit
•Ice Shard
•Low Kick
•Night Slash
Tyranitar - Sand Stream - Life Orb
•Payback
•Pursuit
•Low Kick
•Stone Edge

Note: Illusion does not currently work in Pokémon Essentials.

Once you've beaten all of the gym leaders, return to the Distortion World to where you fought Giratina. Enter the black blob and proceed from there. The band teaches Relic Song to Meloetta. You'll also have one final legendary encounter. Which one? Well you'll see!

That's it! Hope you enjoyed playing!