Breath of the Wild's two endings explained
Breath of the Wild's ending isn't all that special in many ways, but it does have some unique quirks that allow you to skip a lot of quests.

Breath of the Wild's ending probably didn't come as a surprise to many players, with Link defeating Ganon and saving the eponymous princess once again. Still, with The Legend of Zelda: Tears of the Kingdom on the horizon, it might be worthwhile for some players to review the details of Breath of the Wild's ending.
First, it should be noted that Breath of the Wild has multiple endings. The differences between them are negligible, with only a brief cutscene separating BOTW's true ending from the standard one. To get the true ending, the player must simply find all of Link's forgotten memories from before Ganon's rise to power, scattered in certain locations across Hyrule. Players are left to find these locations on their own, with the only hint being a series of photos on their Sheikah Slate.
How To Get BOTW's True Ending

Finding the lost memory location in BOTW unlocks a cutscene that takes place before the fall of Hyrule and provides additional traits for Zelda and the Champions. Other than the extra story content, no benefit comes from finding these memories, so it's probably not worth it to complete this part of the game Anyone but those most interested in the story of Breath of the Wild.
Most of the game's final events play out the same way whether or not the player finds these memories and completes the associated quest "Captured Memories". Link chooses to don his best gear and, with the help of four mythical beasts, ventures into Hyrule Castle, where Calamity Ganon has been sealed away for 100 years.
The Main BOTW Ending

Once the player reaches the center of the castle, they can finally face Cannon himself. If the player completes any of the mythical beasts, their magical energy will shoot towards Hyrule Castle and drain Ganon's overall health. However, like finding all the memories, completing the Beast Dungeon in BOTW is not required to progress through the story.
In fact, if players wish to be challenged by Ganon, they may wish to avoid some or all of these dungeons before defeating him. Either way, Link will eventually have to face Calamity Ganon, who manifests as a cyborg hybrid of a sub-form he found in the mythical beast. Assuming the player has enough gear and practiced the game mechanics, Calamity Ganon should pose No major challenges. He will fall like any other evil beast that roams the continent of Hyrule.
When this happens, Zelda's voice calls out to Link and grants him the Bow of Light. With his trusty steed and steady aim, Link must ride around Ganon and fire arrows of light at his glowing weak spots, much like how players take down mythical beasts. Over time, this version of Ganon also falls, and once Black Beast Ganon is defeated, Zelda will finally emerge after 100 years of relentless efforts to stop him.
Using her Goddess powers, Zelda will seal Calamity Ganon away forever (or at least until he inevitably returns again). Afterwards, she would turn to the hero, thank him for his service, and ask him if he remembered her. On top of Hyrule Castle, the spirits of Hyrule's kings and champions proudly look down on the heroes.
BOTW's Secret Ending Cutscene

If the player has collected all the memories, an additional cutscene will play - The Legend of Zelda: Breath of the Wild's True Ending - depicting Link and Zelda observing the landscape before them. Watch the true ending of Breath of the Wild For yourself in BeardBear's YouTube video:
Both of them admit that even though they've defeated Ganon, there's still a lot of work to be done to fix Hyrule. Given the recent Tears of the Kingdom gameplay trailer (below), it appears that part of that effort will involve building vehicles, but it looks like the evil hasn't quite left this world just yet.
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