This usually relates to the new characters you get during the events in different phases.  Here is for Multiverse:

Action Star Peter: An Action Star is Born

Earn Action Star Peter

(Reward: 5 Vials of Plasma, 100 XP)

Part 1:
Have Action Star Peter Fire at Will: 1 Hour
(Reward: 5 Vials of Plasma, 100 XP)

Part 2:
Have Action Star Peter Take His Shirt Off: Requires Level 2: 6 Hours
(Reward: 5 Vials of Plasma, 100 XP)

 


 

Action Movie Quagmire: Limited Fan Engagement

Part 1:
Have Action Movie Quagmire Pump Iron: 1 Hour
(Reward: 10 Vials of Plasma, 100 XP)

Part 2:
Have Action Movie Quagmire Do the Action Movie Giggity: 8 Hours
(Reward: 10 Vials of Plasma, 100 XP)

Part 3:
Have Action Movie Quagmire Admire His Reflection: 6 Hours
(Reward: 10 Vials of Plasma, 100 XP)

 

 


 

Li’l Lois: Li’l Lolita

Part 1:
Have Li’l Lois Li’l Tai Jitsu: 2 Hours
(Reward: 50 Coins, 25 XP)

Part 2:
Have Li’l Lois Li’l Dance: 4 Hours
(Reward: 50 Coins, 25 XP)

Part 3:
Have Li’l Lois Enjoy Boy Band: 12 Hours
(Reward: 50 Coins, 25 XP)

Part 4:
Have Li’l Lois Bask in Popularity: 8 Hours
{Reward: 150 Coins, 75 XP)


I do not have the quest chains for Li’l Giant Chicken or Li’l Peter as I already had them.  If you have their quest chains, let me know.