Internet Icon Quest Pro Tips
Task 4 involves getting 3 stars at a party so if you have a party that's in progress that you're attending, don't finish all of your first actions until you get to this task, and you should reserve one of your two parties for the beginning of the event so that you don't need to delay a day.
Task 8 is to start a new hobby, so if you have all four sim slots filled and you have not unlocked piano, you will need to retire a sim or buy the piano hobby if you want to continue.
Task #10 is to complete your to-do list so try to hold that off until you get to that task.
Task 12 is to complete your to-do list again so you are assured to face a one day pause.
The longer tasks should be completed by sims with the Good Upbringing trait which cuts the 8 hour duration by 24 minutes. I don't think there is any other way to cut the duration of these tasks.
Okay, here you go!
Video Walkthrough:
Part 1: https://youtu.be/TwEFVJRmCaA
Part 2: https://youtu.be/JeghglxuNv4
Text Walkthrough:
Part 1 of 18 - Get Spiffed Up For Fans
Tip: Take a Shower and click the blue Event.Part 2 of 18 - Ask 3 Sims About Simstagram.
Tip: Tap any Sim who is not a stranger and tap the blue Event. If the Sim is a stranger, simply introduce yourself first.Part 3 of 18 - Start A Friendly Story.
Tip: Tap any Sim you are not already friends with and tap "Begin A Friendship". Once you complete that event you'll be prompted to select a story, and that will complete this Part.Part 4 of 18 - Earn 3 Stars At A Party.
Tip: Go to any party and earn three stars by interacting with other sims. If you have already completed there stars, simply visit the active party to complete the Part.Part 5 of 18 - Earn 650 Simoleons.
Tip: Complete Hobby events or send your Sims to work to earn Simoleons.Part 6 of 18 - Complete 3 Relationship Events.
Tip: Tap on friends or family and trigger the pink Events to complete this. These usually take up to an hour each.Part 7 of 18 - Complete the Fashion Icon Event.
Tip: Tap on a couch or loveseat to begin this event. Your sim will be transported to Market Square. The event takes 8 hours to complete, or you can fast-forward it for 93 Sim Cash. This is not linked to the Fashion Designer career, you can use any Sim.Part 8 of 18 - Start A New Hobby
Tip: You just need to START a hobby, you don't need to do anything else.Part 9 of 18 - Complete the Fan Club Event.
Tip: Tap on a couch or loveseat to begin this event. Your sim will be transported to Downtown. The event takes 8 hours to complete, or you can fast-forward it for 93 Sim Cash.Part 10 of 18 - Complete the Daily To Do List.
Part 11 of 18 - Complete the Biz Event.
Tip: Tap on a couch or loveseat to begin this event. Your sim will be transported to Downtown. The event takes 8 hours to complete, or you can fast-forward it for 93 Sim Cash.Part 12 of 18 - Complete the Daily To Do List again.
Part 13 of 18 - Earn 20 Sim Tickets.
Tip: Complete any interactions with other sims to earn Sim Tickets, go to Parties, or watch ads.Part 14 of 18 - Complete the Fashion Icon Event.
Tip: See above.Part 15 of 18 - Buy New Clothing/Apparel.
Tip: Pretty simple, just gotta buy three new pieces of clothing... if you haven't already got everything!Part 16 of 18 - Complete the Fan Club Event.
Tip: See above.Part 17 of 18 - Complete 2 Hobby Story Chapters.
Tip: These are the little sub-missions that pop up at levels 3, 5, 7, and 10 of any career or hobby. You need to complete any two. Doing two of the Level 3 ones on different sims works fine.Part 18 of 18 - Complete the Fashion Icon Event.
Tip: See above.