You can only start The Take-Over Continues if you've completed both A Troubling Situation and any unfinished Giovanni Special Research quests, such as December's A Challenging Development.
The Take-Over Continues 1/6
- Spin 10 PokéStops (Encounter with Sudowoodo)
- Defeat 3 Team Go Rocket Grunts (500 XP)
- Catch 1 Shadow Pokémon (500 XP)
Rewards: 500 Stardust, 10 PokéBalls and 10 Razz Berries
The Take-Over Continues 2/6
- Spin a PokéStop 3 days in a row (750 XP)
- Purify 5 Shadow Pokémon (750 XP)
- Win 5 Raids (750 XP)
Rewards: 1,000 Stardust, 3 Hyper Potions and 3 Revives
The Take-Over Continues 3/6
- Use 6 super effective charge attacks in Gym battles (1,000 XP)
- Win 3 Great League Trainer Battles against another Trainer (1,000 XP)
- Defeat 6 Team Go Rocket Grunts (1,000 XP)
Rewards: 1,500 Stardust, 15 Great Balls and 5 Pinap Berries
The Take-Over Continues 4/6
- Defeat Team Go Rocket Leader Arlo (1,250 XP)
- Defeat Team Go Rocket Leader Cliff (1,250 XP)
- Defeat Team Go Rocket Leader Sierra (1,250 XP)
Rewards: 2,000 XP, Super Rocket Radar and 3 Golden Razz Berries
The Take-Over Continues 5/6
- Find the Team Go Rocket Boss (2,500 Stardust)
- Fight the Team Go Rocket Boss (1,500 XP)
- Defeat the Team Go Rocket Boss (3 Silver Pinap Berries)
Rewards: 3,000 Stardust, 1 Fast TM and 1 Charged TM
The Take-Over Continues 6/6
All three challenges for this step will have automatically been completed, allowing you to collect 2,000 XP for each one. This means that you'll collect 6,000 XP in total.
Rewards: 3 Max Revives, 3 Rare Candies and 20 Ultra Balls