This page of the guide to Final Fantasy 7 Remake has a walkthrough for the Chocobo Search side mission available in Chapter 14 - In Search of Hope.
The task will begin upon talking to the doctor. He will ask you to gather herbs to produce medicines. Let's start with the first herb in the church. You could have gotten them already by completing Corneo's Secret Stash or Tomboy Bandit missions.
The second item you need can be purchased at the Moogle Emporium at Kids Hideou.
The final task will be to complete the Subterranean Menace a side mission. According to the premise of this mission, you must defeat the boss - Type 0 Behemoth. After eliminating your opponent, you get the last ingredient and you can go back to the doctor and complete the quest.
Reward: Aerith skill points.