Celebi Research Requirements

We now know the first 6 quests for A Ripple in Time. Once the last two become available, I will update this list. Good luck in your search for Celebi!
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Update: We now know all 8 quests to catch Celebi! It appears that there is really only 7 quests to be done. Then, after catching Celebi, the final quest is automatically completed with more rewards and additional dialog from Professor Willow.

Quest (1/8)

Tasks:

• ​Power up Pokemon 5 times
• Battle in a gym 2 times
• Battle in a raid

Rewards:

• 10 Pokeballs
• a Fast TM
• a Special Incubator

Quest (2/8)

Tasks:

• ​Make 3 new friends
• Evolve an evolved Grass-Type Pokemon
• Catch a Pokemon 3 days in a row

Rewards:

• ​​1500 Stardust
• a Sunstone
• a Premium Raid Pass

Quest (3/8)

Tasks:

• ​Reach Level 25
• Use a Sunstone to evolve Gloom or Sunkern
• Hatch 9 Eggs

​Rewards:

• an Eevee encounter
• a King's Rock
• a Premium Raid Pass 

Quest (4/8)

Tasks:

• ​Walk 10km with Eevee as your Buddy to earn candy
• Evolve Eevee into Espeon during the day
• Send 20 gifts to friends

​Rewards:

• 1500 Stardust
• a Sunstone
• a Premium Raid Pass

​Quest (5/8)

Tasks:

• ​​Walk 10km with Eevee as your Buddy to earn candy
• Evolve Eevee into Umbreon at night
• ​Trade a Pokemon

​Rewards:

• a Starpiece
• 15 Pinap Berries
  
• ​an Upgrade
  

​Quest (6/8)

Tasks:

• Visit Pokestops 7 days in a row
• Use 25 Pinap Berries while catching Pokemon
• Use items to evolve Pokemon 2 times

Rewards:​

• 3500 Stardust
• a Dragon Scale
  
• ​5 Silver Pinap Berries
  

Quest (7/8)

Tasks:

• ​Catch 40 Grass- or Psychic-type Pokemon
• Make an Excellent Curveball Throw
• Earn a gold Johto medal

Rewards:​

• 10 Silver Pinap Berries
• a Charge TM
• ​Celebi encounter

Quest (8/8)

Tasks:

• Auto Completed Quest
• Auto Completed Quest
• Auto Completed Quest

Rewards:​

• 20 Celebi Candy
• a Super Incubator
• ​5500 Stardust