Simple Elimination

Category 1: Pokemon Types - Water
Category 2: Game Mascots - Ho-Oh
Category 3: Non-Plate/incense, non-specific-Pokémon type enhancing items - Miracle Seed
Category 4: Berries that lower effectiveness of moves - Roseli Berry
Category 5: Poké Balls - Timer Ball
Category 6: Pokémon with a BST of 525 - Glaceon
Category 7: Pokémon in the Black Colour Category - Giratina
Category 8: Pokémon in only the Monster Egg Group - Aron
Category 9: Towns/Cities with Gyms - Opelucid City
Category 10: Pokémon in the Mineral Egg Group - Klefki
Category 11: Starter Final Evos - Sceptile
Category 12: Pokémon that have had their type changed - Gardevoir
Category 13: Friend Areas - Healing Forest
Category 14: Elite Four Members - Sidney
Category 15: Abilities that start with S - Storm Drain
Category 16: Pokemon with Body Style classification of "Only a Head" - Cryogonal
Category 17: Electric-type moves (excluding Z-moves) - Bolt Strike
Category 18: Pokémon in the Erratic experience group - Lumineon
Category 19: Evolution-inducing locations (core series) - Chargestone Cave
Category 20: Pokémon with Psychic as a secondary type - Latias/Mega Latias
Category 21: Generation I TMs - TM13 Ice Beam 
Category 22: Pokémon that can know the move "Switcheroo" - Linoone
Category 23: Pokémon that have a Winged Insectoid body style (Body Style 13) - Beautifly
Category 24: Non-legendary, Non-mega Pokémon with a base Attack stat higher than 130 (by Gen 7 stats) - Salamence
Category 25: Trainer Classes beginning with 'B' - Battle Girl
Category 26: Pokémon with a BST of 305 - Ducklett
Category 27: Pokémon with unique type combinations - Giratina
Category 28: Battle Facility Leaders - Pike Queen Lucy
Category 29: Pure Fire-type Pokémon - Rapidash
Category 30: Pokémon Natures - Gentle
Category 31: Pokémon that weigh 150-199.9kg - Walrein
Category 32: Moves that can cause Confusion - Water Pulse
Category 33: Trainer Classes of Gen 1 - Cooltrainer
Category 34: Pokémon with the Levitate Ability - Latias
Category 35: Evolution-inducing held items - Prism Scale
Category 36: Pokémon with Categories that begin with 'A' - Skarmory (Armor Bird Pokémon)
Category 37: Pokémon in the 'Fast' Experience Group - Alomomola
Category 38: Pokémon with a unique evolution method - Feebas
Category 39: Gym Leaders (Pre-Gen 8) - Clair
Category 40: Pokémon without Hidden Abilities
(Part 1 of 3 - A-G) - Flygon
(Part 2 of 3 - H-R) - Latias
(Part 3 of 3 - S-Z) - Vibrava
Category 41: The Plates of Arceus - Sky Plate
Category 42: Pure Ground Type Pokémon - Trapinch
Category 43: Main Series Player Characters - May
Category 44: Pokémon that can know the move "Rototiller" - Linoone
Category 45: Pokémon with a BST of 455 - Swellow
Category 46: Non-Power-Reducing, Non-E-Reader Berries - Sitrus Berry
Category 47: Pokémon with a Catch Rate of 60 - Milotic
Category 48: Item-manipulating moves - Thief
Category 49: Body style 14 Pokémon ("insectoid") - Trapinch