Heres a full list, gonna keep it short and sweet as possible! Optional Characters at the end. Note, Quests such as Bonus hearts 1/2 are unlocked via various sidequest clears. If anything is noticeably difficult or obscure I'll list them here.

Link : You start the game with him obvs. Spear Moveset: Unlocked as soon as you obtain a spear weapon (can be done in Ch2 onwards) 2h Moveset: Same as Spear, CH2 onwards. Master Sword : Unique 1h weapon. Enables Blade Beam at Max health, obtained in Ch3 mission: Freeing the Korok Forest.

Impa: Obtained during the first mission: The Battle of Hyrule Field, as soon as the Fire Wizzrobe appears

Zelda: Obtained partway thru the second mission, after the 2nd inactive Guardian shoots at the enemy, starts with Sheikah Slate moveset. Ch3/4 depending on how often you do sidequests you'll unlock her Quests to increase sheikah slate powers. Enhance Ability is unlocked during Ch7. Bow of Light: Unlocked during Ch6, Each Step Like Thunder quest. Extra quests for BoL moveset unlocked during Ch7, after Bow of Light Training

Mipha: Unlocked after the Ch2 quest, Mipha the Zora Princess. Her moveset quests is unlocked immediately after obtaining her, with an extra moveset piece locked behind Mipha's Training.

Daruk Unlocked after the Ch2 Quest, Daruk the Goron Hero. Quests for moveset identical to Mipha requirements. Both him and Yunobo have a heart and enhance quest hidden behind joint challenge and Anti Fire line of quests

Urbossa Unlocked after Ch2 Quest, Urbossa the Geruda Chief Quests similar to Mipha. She has a quest to enhance ability unlocked after some challenges with her and Riju, as well as the Anti Thunder challenge questline

Revali Unlocked immediately after finishing Ch2 Quest, Revali the Rito warrior. Quests similar to Mipha. Has a bonus heart trigger hidden behind Revali and Tebu joint challenges

Hestu Unlocked via clearing the Ch3 quest, Freeing Korok Forest. His Quest line is hidden behind obtaining Korok seeds obtained by finding korok strewn throughout the main story. Note, there is also a Dancing Challenge that hides his final moveset, and Korok seeds are also used to expand inventory

Sidon: obtained during the Ch5 Quest Water and Fire after clearing the initial fight vs Waterblight Ganon. He has bonus hearts hidden behind a questline with him and Mipha.

Yunobo: Obtained upon clearing Ch5 Quest Water and Fire after the fight vs Fireblight Ganon. See Daruk for info on his moveset.

Teba: Obtained after clearing Ch5 Quest, Air and Lightning, After defeating Windblight Ganon. Moveset hidden behind Training quest, and Crossing the Hebu Valley challenge.

Riju : Obtained during the Ch5 Quest, Air and Lightning, after defeating Thunderblight Ganon. Moveset locked behind the Antithunder challenge and Ladies tournament questline.

Master Kohga: Obtained during Ch6 immediately after Zelda gains the bow of light. His moveset and bonus hearts are hidden behind the Koga Clan fights unlocked in Ch5.

King Rhoam Obtained after clearing The Great Plateau. His moveset was entirely unlocked for me at the start, so I dont really have an answer for this one. Sorry.

Great Fairies Obtained after clearing the 4 Great Fairy battlefields, unlocked at the beginning of Ch3 after clearing the delivery Offering Help on the Road

Monk Maz Koshia Obtained after clearing Vs Monk Maz Koshia which is revealed after qualifying for the Trial upon clearing the Trial of Monsters, Trial of Stones and Trial of the Mighty Foe Quests.

Terrako Obtained at the end of Ch7 after clearing the game, and obtaining all 50 Terrako pieces by clearing the various quests that unlock.

Calamity Ganon Obtained by clearing the Vs Calamity Ganon quest. You unlock this quest by: Finishing the game, Clearing all the Challenge Vs quests (Monk Maz, Harbinger Ganon, Astor, and the Arena/Coliseum quests), and the Endgame questline where its various timed quests vs Malice enemies: Mysterious Arrivals, Defend Hyrule Castle, Harbingers of Calamity, Defend Akala Citadel, The Guardians Counter Attack