Get the following Special tickets by releasing the corresponding combination of Pokemon:

Articuno - Pidgeot, Fearow, Jynx, and Lapras
Burmy Sand/Trash Cloak - Five Mothims
Cut Rotom - Rotom and Leafeon
Darkrai - Wash Rotom, Heat Rotom, Spin Rotom, Cut Rotom, and Frost Rotom
Dialga - Dragonite, Bastiodon, Lucario, Garchomp, and Magnezone
Frost Rotom - Rotom and Glaceon
Gastrodon West Sea - Five Shellos East Seas
Giratina - Gengar, Dragonite, Garchomp, Spiritomb, and Dusknoir
Heat Rotom - Rotom and Flareon
Manaphy - Three Phiones
Mewtwo - Dialga, Palkia, and Giratina
Moltres - Charizard, Pidgeot, Fearow, and Magmar
Palkia - Blastoise, Gyarados, Dragonite, Empoleon, and Garchomp
Phione - Lapras and Vaporeon
Shaymin - Arcanine, Charizard, Kangaskhan, Bastiodon, and Arbok
Shellos West Sea - Five Gastrodon East Seas
Spin Rotom - Rotom and Jolteon
Wash Rotom - Rotom and Vaporeon
Wormadam Sand/Trash Cloak - Five Burmy Grass Cloaks
Zapdos - Pidgeot, Fearow, Raichu, and Electabuzz