In order to get certain Pokémon in this game, you have to exchange a variety of Pokémon Toys for these Pokémon. As such, you have to collect as many as you can within the various levels. Once you've released the specific Pokémon, you may get a ticket. Go over to the Random Recruiting part of the Terminal and you'll get another Pokémon. The tickets we know of are as follows

Pokémon Given Away Ticket Received
5 of the same Pokémon Evolution of the Pokémon you released
Rotom & Vaporeon, Flareon, Jolteon, Leafeon or Glaceon Alternate Rotom Form;
Wash Rotom if Vaporeon
Heat Rotom if Flareon
Fan Rotom if Jolteon
Mow Rotom if Leafeon
Frost Rotom if Glaceon
Lapras, Jynx, Pidgeot & Fearow Articuno
Raichu, Electabuzz, Pidgeot & Fearow Zapdos
Charizard, Magmar, Pidgeot & Fearow Moltres
Dialga, Palkia & Giratina Mewtwo
Lucario, Bastiodon, Magnezone, Dragonite & Garchomp Dialga
Blastoise, Gyarados, Empoleon, Dragonite & Garchomp Palkia
Gengar, Spiritomb, Dusknoir, Dragonite & Garchomp Giratina
Lapras & Vaporeon Phione
Phione x3 Manaphy
Fan Rotom, Frost Rotom, Heat Rotom, Mow Rotom, Wash Rotom Darkrai
Arbok, Charizard, Kangaskhan, Bastiodon & Arcanine Shaymin
 
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