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.
5 Star Servants Tier List: Best Servants [5★]
Best Servants [★4]: 4 Star Tier List
1-3 Star Servants Tier List
Valentine event: Chocolate Lady's Commotion [US 2018]
Nero Claudius (Bride)
FGO Reroll Tier List
Jack the Ripper
Talk on the Heated Sands
Street Choco Maid
Kitchen ☆ Patissiere
Holy Night Supper