Skill Up & Ascension MaterialProof that you've been acknowledged as a hero. Many possess it, but they aren't conscious of it so they forget.
Okeanos: Pirate Ship (Free Quest) is the best AP-saving & time-saving location to farm Hero's Proof (Proof of Hero). You'll get around 6x Hero's Proof by spending 120AP.
Here is a list of servants that need Hero's Proof to perform Ascension or Skill-Up.
]Journey to the West Event Re-run
Hunting Quest Part 1
Fate/Accel Zero Order Advance Campaign
Fate/Accel Zero Order Event
Lostbelt No.1: Anastasia
5 Star Servants Tier List: Best Servants [4/13 updated!]
Best Servants [★4]: 4 Star Tier List
1-3 Star Servants Tier List
Best Craft Essence: Craft Essence Tier List
Ivan the Terrible (Ivan the Thunder Emperor)
FGO Reroll Tier List
Anastasia Nikolaevna Romanova
Irisviel (Dress of Heaven)
Ramesses II (Ozymandias)
Black Holy Grail (The Black Grail)
Talk on the Heated Sands
Nine-Headed Bull Demon King
Lunar Hot Springs