Here's a list of spirits I think one must summon in order to gain (93 in total). Other summonable spirits can be found either in the World of Light or in one of the shops (vault shop or WoL shops). The spirits you need to sacrifice can be found there, too (with one notable exception). Spirits marked with an Asterisk (*) can be evolved into another exclusive spirit. After you summoned a spirit, it can appear on the Spirit Board and maybe even in shops.
It's possible that some spirits I've listed are not exclusive to summoning and that I had just some bad luck. Further input would be appreciated. If it doesn't appear on the list, I've gotten it elsewhere. Take note that at least some spirits, once they've been summoned, start to appear on the Spirit Board as well. I'm still positive that the spirits in question wouldn't have appeared before I summoned them.
By the way: When you give up a spirit of which you had only that one exemplar, there's a higher chance that this spirit re-appears in the Spirit Board or in the particular shop in which it is sold.
#24 Gold Mario - Metal Mario + Super Mushroom + Fire Flower
#28 Cat Princess Peach - Rover + Baby Peach
#45 Birdo - T-Rex + Starly
#52 Thwomp - Rock-Pikmin + Rocky
#64 Nabbit - Duster + random sub
#66 King Bob-Omb - Bob-Omb + Shake King
#70 Shadow Mario - Vince + Eddy + random neutral
#76 Sprixie Fairies - Wanda + Princess Shokora
#78 Cappy - Ezlo + Boo-Mario
#93 Master Cycle - Mach Rider + City Tripper + Excitebike + random attack
#94 Paper Mario - Cut Man + Cardboard Box + random neutral
#99 Shadow Queen - Vivian + Gengar
#120 Professor Elvin Gadd - Poltergust 5000 + F.L.U.D.D.
#143 Dixie Kong* - Tiny Kong + Candy Kong
#163 Baron K. Roolenstein - Dr. Cygor + Kritter + The Creature & Fleaman
#196 Epona - Rapidash + Malon
#200 Ruto - Zora + Princess Shokora + random defence
#202 Koume & Kotake* - Charlotte Aulin + Froster + Fire Flower
#210 Moon - Majora's Mask + random sub
#230 Demise - The Imprisoned + Ghirahim
#313 Super Happy Tree - Whispy Woods + Bonus Fruit + random neutral + 2x random sub
#345 Dyna Blade - Super Star + Beat + Cucco + random defence
#351 Daroach* - Count Cannoli + Mouser + 2x random neutral
#353 Masked Dedede - Reporter & Wrestler + Hammer Bro
#354 Galacta Knight - Shovel Knight + Knight Man + Meta-Knights
#357 Queen Sectonia - Zinger + Princess Shroob
#375 Mr. Shine & Mr. Bright - Baxter & Forthington + Slugger & Green Glove
#391 Great Fox - Landmaster + Arwing + random neutral + random sub
#400 Andross (Star Fox) - Porygon + Commander
#467 Togepi - Gordo + Mega Egg
#476 Scizor - Zebesian + Sidestepper
#501 Jirachi - Star Rod + Luma + Starlow
#532 Kyurem (Black Kyurem) - Reshiram + Kyurem
#533 Kyurem (White Kyurem) - Zekrom + Kyurem
#577 Mr. Saturn - Specknose + Qbby
#587 Ultimate Chimera - Blargg + Pyoro
#588 Absolutely Safe Capsuke - Mr. Saturn + 6x random defence
#594 Samurai Goroh - Takamaru + Sakura Samurai + Tac + random attack
#648 Hector (Fire Emblem) - Lilina + random sub
#654 Ephraim - Frey & Freya + Eirika
#666 Micaiah - Sothe + Pitch + random grapple
#669 Cordelia - Severa + Kaitlin & Katie
#682 Xander - Leo + Camilla + Elise
#698 Octopus - Octoman + Octorok + Oil Panic + 2x random defence
#699 Chef (Game & Watch) - Chef (Personal Trainer: Cooking) + Huey + random sub
#706 Pit (Original) - Centurion + Cupid + random grapple
#724 Phosphora - Elec Man + Rotom
#731 Jimmy T. - Don Flamenco + Kalypso
#732 Mona - Quendan-Cheergirls + Ayumi Tachibana
#765 Raiden - Solidus Snake + Rosemary + 3x random attack + random neutral
#781 Knuckles - Gordo + Muddy Mole + random grapple
#794 Jet the Hawk - Pidgey + Akari Hayami
#796 Sonic the Werehog - Togedemaru + Werewolf
#800 Louie - Snorlax + Postman + random grapple
#813 Burrowing Snagret - Raphael the Raven + Rattly the Rattlesnake
#814 Plasm Wraith - Hakkun + Eddy + random neutral
#828 Tom Nook* - Maruhige Shop Owner + Shop Assistent + random neutral
#831 DJ K.K.* - 9-Volt & 18-Volt + Labrador Retriever
#833 Resetti - Mettaur + Dugtrio + Muddy Mole + 2x random attack
#839 Pete - Cucco + Postman + random sub
#840 Phyllis & Pelly - Mio & Mayu Amakura + Pitch
#845 Tortimer - Old Man Lobber + Koopa + random sub
#849 Blathers - T-Rex + Beetle + Fishman
#865 Proto Man - Dr. Light + Roll + random defence
#869 Rush - Chibi-Tot + Boney + random sub
#882 Yellow Devil - Waddle Doo + Diskun
#928 Tree (Wii Fit) - Whispy Woods + Sudowoodo
#930 Warrior (Wii Fit) - Seliph + Heracles
#940 Super Macho Man - Machamp + Balrog + Urban Cahmpion Fighter + random attack
#947 Mother Fairy - Great Fairy + Fairy Bottle
#965 Formula - Mech + Robobot Armor
#979 E. Honda - Sumo Bros. + Piston Hondo
#985 Dhalsim - Fire Man + Great Tiger#1037 Flow - Shop Assistent + Madame Couture
#1001 Ibuki - Shinobu + Ayumi Tachibana
#1002 Yun & Yang - Mio & Mayu Amakura + Young Cricket
#1012 Rodin* - Brewster + Aegislash
#1027 Inkling Squid - Blooper + Huey + random sub
#1028 Judd - Judge + Meowth + random neutral + random sub
#1030 Squid Sisters - Blooper + Meloetta (Aria Form) + Quendan-Cheergirls
#1036 Spyke - Big Urchin + Unira
#1043 D.J. Octavio* - Octoling + Octorok + random neutral
#1062 Julius Belmont - Juste Belmont + Reinhardt Schneider
#1104 Master Core - Master Sabres + Master Beast + Master Giant
#1181 Starfy - Moe + Old Man Lobber + Mermaid
#1190 Jill & the Drill Dozer - Duster + Drill Man
#1193 The Wandering Samurai* - Sakura Samurai + random defence
#1211 Barbara the Bat - Rouge the Bat + Prince Saruno + random grapple
#1262 Dillon - Wheelie + Sandshrew + random attack
#1283 Wonder-Red - Wonder-Blue + Drake Redcrest
#1288 Ribbon Girl - Elite Beat Divas + Chuchu
#1291 Ninjara - Shinobu + Shadow Man
It's possible that some spirits I've listed are not exclusive to summoning and that I had just some bad luck. Further input would be appreciated. If it doesn't appear on the list, I've gotten it elsewhere. Take note that at least some spirits, once they've been summoned, start to appear on the Spirit Board as well. I'm still positive that the spirits in question wouldn't have appeared before I summoned them.
By the way: When you give up a spirit of which you had only that one exemplar, there's a higher chance that this spirit re-appears in the Spirit Board or in the particular shop in which it is sold.
#24 Gold Mario - Metal Mario + Super Mushroom + Fire Flower
#28 Cat Princess Peach - Rover + Baby Peach
#45 Birdo - T-Rex + Starly
#52 Thwomp - Rock-Pikmin + Rocky
#64 Nabbit - Duster + random sub
#66 King Bob-Omb - Bob-Omb + Shake King
#70 Shadow Mario - Vince + Eddy + random neutral
#76 Sprixie Fairies - Wanda + Princess Shokora
#78 Cappy - Ezlo + Boo-Mario
#93 Master Cycle - Mach Rider + City Tripper + Excitebike + random attack
#94 Paper Mario - Cut Man + Cardboard Box + random neutral
#99 Shadow Queen - Vivian + Gengar
#120 Professor Elvin Gadd - Poltergust 5000 + F.L.U.D.D.
#143 Dixie Kong* - Tiny Kong + Candy Kong
#163 Baron K. Roolenstein - Dr. Cygor + Kritter + The Creature & Fleaman
#196 Epona - Rapidash + Malon
#200 Ruto - Zora + Princess Shokora + random defence
#202 Koume & Kotake* - Charlotte Aulin + Froster + Fire Flower
#210 Moon - Majora's Mask + random sub
#230 Demise - The Imprisoned + Ghirahim
#313 Super Happy Tree - Whispy Woods + Bonus Fruit + random neutral + 2x random sub
#345 Dyna Blade - Super Star + Beat + Cucco + random defence
#351 Daroach* - Count Cannoli + Mouser + 2x random neutral
#353 Masked Dedede - Reporter & Wrestler + Hammer Bro
#354 Galacta Knight - Shovel Knight + Knight Man + Meta-Knights
#357 Queen Sectonia - Zinger + Princess Shroob
#375 Mr. Shine & Mr. Bright - Baxter & Forthington + Slugger & Green Glove
#391 Great Fox - Landmaster + Arwing + random neutral + random sub
#400 Andross (Star Fox) - Porygon + Commander
#467 Togepi - Gordo + Mega Egg
#476 Scizor - Zebesian + Sidestepper
#501 Jirachi - Star Rod + Luma + Starlow
#532 Kyurem (Black Kyurem) - Reshiram + Kyurem
#533 Kyurem (White Kyurem) - Zekrom + Kyurem
#577 Mr. Saturn - Specknose + Qbby
#587 Ultimate Chimera - Blargg + Pyoro
#588 Absolutely Safe Capsuke - Mr. Saturn + 6x random defence
#594 Samurai Goroh - Takamaru + Sakura Samurai + Tac + random attack
#648 Hector (Fire Emblem) - Lilina + random sub
#654 Ephraim - Frey & Freya + Eirika
#666 Micaiah - Sothe + Pitch + random grapple
#669 Cordelia - Severa + Kaitlin & Katie
#682 Xander - Leo + Camilla + Elise
#698 Octopus - Octoman + Octorok + Oil Panic + 2x random defence
#699 Chef (Game & Watch) - Chef (Personal Trainer: Cooking) + Huey + random sub
#706 Pit (Original) - Centurion + Cupid + random grapple
#724 Phosphora - Elec Man + Rotom
#731 Jimmy T. - Don Flamenco + Kalypso
#732 Mona - Quendan-Cheergirls + Ayumi Tachibana
#765 Raiden - Solidus Snake + Rosemary + 3x random attack + random neutral
#781 Knuckles - Gordo + Muddy Mole + random grapple
#794 Jet the Hawk - Pidgey + Akari Hayami
#796 Sonic the Werehog - Togedemaru + Werewolf
#800 Louie - Snorlax + Postman + random grapple
#813 Burrowing Snagret - Raphael the Raven + Rattly the Rattlesnake
#814 Plasm Wraith - Hakkun + Eddy + random neutral
#828 Tom Nook* - Maruhige Shop Owner + Shop Assistent + random neutral
#831 DJ K.K.* - 9-Volt & 18-Volt + Labrador Retriever
#833 Resetti - Mettaur + Dugtrio + Muddy Mole + 2x random attack
#839 Pete - Cucco + Postman + random sub
#840 Phyllis & Pelly - Mio & Mayu Amakura + Pitch
#845 Tortimer - Old Man Lobber + Koopa + random sub
#849 Blathers - T-Rex + Beetle + Fishman
#865 Proto Man - Dr. Light + Roll + random defence
#869 Rush - Chibi-Tot + Boney + random sub
#882 Yellow Devil - Waddle Doo + Diskun
#928 Tree (Wii Fit) - Whispy Woods + Sudowoodo
#930 Warrior (Wii Fit) - Seliph + Heracles
#940 Super Macho Man - Machamp + Balrog + Urban Cahmpion Fighter + random attack
#947 Mother Fairy - Great Fairy + Fairy Bottle
#965 Formula - Mech + Robobot Armor
#979 E. Honda - Sumo Bros. + Piston Hondo
#985 Dhalsim - Fire Man + Great Tiger#1037 Flow - Shop Assistent + Madame Couture
#1001 Ibuki - Shinobu + Ayumi Tachibana
#1002 Yun & Yang - Mio & Mayu Amakura + Young Cricket
#1012 Rodin* - Brewster + Aegislash
#1027 Inkling Squid - Blooper + Huey + random sub
#1028 Judd - Judge + Meowth + random neutral + random sub
#1030 Squid Sisters - Blooper + Meloetta (Aria Form) + Quendan-Cheergirls
#1036 Spyke - Big Urchin + Unira
#1043 D.J. Octavio* - Octoling + Octorok + random neutral
#1062 Julius Belmont - Juste Belmont + Reinhardt Schneider
#1104 Master Core - Master Sabres + Master Beast + Master Giant
#1181 Starfy - Moe + Old Man Lobber + Mermaid
#1190 Jill & the Drill Dozer - Duster + Drill Man
#1193 The Wandering Samurai* - Sakura Samurai + random defence
#1211 Barbara the Bat - Rouge the Bat + Prince Saruno + random grapple
#1262 Dillon - Wheelie + Sandshrew + random attack
#1283 Wonder-Red - Wonder-Blue + Drake Redcrest
#1288 Ribbon Girl - Elite Beat Divas + Chuchu
#1291 Ninjara - Shinobu + Shadow Man
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