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.
Rashoumon event (Ibaraki Douji event)
Murder at the Kogetsukan
Inheritance of Glory
5 Star Servants Tier List: Best Servants [5/9 updated!]
FGO Reroll Tier List [5/11 updated!]
1-3 Star Servants Tier List
Best Servants [★4]: 4 Star Tier List
Best Craft Essence: Craft Essence Tier List
Cu Chulainn (Alter, Berserker)
Nero Claudius (Caster, Summer 2017)
Minamoto No Yorimitsu (Lancer, Summer 2017)
Oda Nobunaga (Berserker, Summer 2017)
Hans Christian Andersen
Frankenstein (Saber, Summer 2017)
Sometime in Summer
Piece of Year 2030 (A Fragment of 2030)