When you talk to Purah in the Hateno Town during the Locked Mementos quest you will learn that Princess Zelda took several pictures in the Sheikah Slate album and each memory is tied to your memory of her. You will then receive the Captured Memories quest from Impa. Listed below are all those memories including those found in the main quest, when you arrive at the indicated location you will see a glowing spot that will trigger the memory and unlock it. The following video will show you exactly where all 18 memories can be found.
Memory 1 - Subdued Ceremony
Location: Sacred Ground Ruins, Central Hyrule
Memory 2 - Revali's Flap
Location: Rito Village, Tabantha
This memory is not attached to Princess Zelda and can be obtained during the main quest - Divine Beast Medoh.
Memory 3 - Resolve and Grief
Location: Lake Kolomo, Central Hyrule
Memory 4 - Daruk's Mettle
Location: Goron City, Eldin
This memory is not attached to Princess Zelda and can be obtained during the main quest - Divine Beast Vah Rudania.
Memory 5 - Zelda's Resentment
Location: Ancient Columns, Tabantha
Memory 6 - Urbosa's Hand
Location: Gerudo Town, Gerudo Desert
This memory is not attached to Princess Zelda and can be obtained during the main quest - Divine Beast Vah Naboris.
Memory 7 - Blades of the Yiga
Location: Kara Kara Bazaar, Gerudo Desert
Memory 8 - A Premontion
Location: Eldin Canyon, Eldin
Memory 9 - Silent Princess
Location: Irch Plain, Hyrule Ridge
Memory 10 - Mipha's Touch
Location: Zora's Domain, Lanayru
Memory 11 - Shelter from the Storm
Location: West Necluda, Dueling Peaks
Memory 12 - Father and Daughter
Location: Hyrule Castle, Central Hyrule
Memory 13 - Slumbering Power
Location: Spring of Power, Akkala
Memory 14 - To Mount Lanayru
Location: Sanidin Park Ruins, Hyrule Ridge
Memory 15 - Return of Calamity Ganon
Location: Lanaryu Road - East Gate, Necluda
Memory 16 - Despair
Location: Hyrule Field, Central Hyrule
Memory 17 - Zelda's Awakening
Location: Fort Hateno, Dueling Peaks
Memory 18 - The Master Sword
Location: Korok Forest, Great Hyrule Forest
Although attached to Princess Zelda there is no picture in the Sheikah Slate album. This memory can be obtained during the main quest - The Hero's Sword and you will need at least 13 Heart Containers to pull out the sword and unlock the final memory.