According to gamepedia, a hero will get between 0-5 Hero Merits per battle.
Hero Merit can be obtained by heroes who successfully survive and complete a battle. The hero will then gain anywhere from 0 to 5 Hero Merit depending on the difficulty of the battle based on the number of enemies on the map, the enemy level, and the enemy rarity.
As of right now, an exact formula is not known, however, this thread explains how to get over 500 total Hero Merits a day, as clearing the Tenth Stratum in the Training Tower with 4 5 star Heroes apparently always awards 4.60 Hero Merit per character.
Bringing 4 5 Star Lvl 40 Units into Tenth Stratum gives each unit 4.60 Merit to each. Thanks to the 99 stamina cap its more plausible to use all of the natural stamina given each day.
((24 Hours x 60 Minutes)/5 Regen Timer) = 288 StaminaPerDay
That lets us do the Tenth Stratum 32 times a day. Assuming no deaths, each time you do Tenth Stratum you gain 147.2 Merit for each unit or a total of 588.8.
It will take approximately 13.58 days to get 4 units to 2000 Hero Merit each. Meaning an average day of Tenth Stratum gives 589 feathers.