The FameStar feature may go down periodically. It seems the Weekly challenges reset around Wednesday.
Many people have had issues with this not popping on Bonus Challenges alone, and had to complete new Weekly Challenges for it to finally register.
Here's the Bonus Challenge list for Home Run Stars:
(and the Fame Points they are worth)
Invite a friend to an Xbox Live Duel and throw a Perfect Pitch - 50FP
Score an Epic Home Run in any stadium - 50FP
Activate and score 3 multipliers in a stadium - 75FP
Hit the Jumbotron 10 times in any stadium - 100FP
Play 10 Duel matches wearing the Franchise Player costume - 100FP
Anger the Dragon by hitting him 3 times in a game - 100FP
Score 2,000,000 points while wearing the King of Home Runs costume - 150FP
Earn 5,000,000 total points - 150FP
Play 25 Xbox Live Duel games - 200FP
Play Home Run Stars for the first time - 25FP
* to get a Perfect Pitch, you must be in a Duel match - as the pitcher, select 1 of the 3 pitch types, then throw the ball using your arm while the meter slider is in the small green part of the meter
* to get an Epic Home Run, get a Perfect Hit and then aim the ball out of the stadium without hitting any targets
* to Anger the Dragon, get 3 Perfect Hits and then aim each at the Dragon head, must be done in one game
* the Franchise Player costume is unlocked for anyone that is FameStar level "Up & Coming" or above; you must go to the FameStar Rewards menu and then select the costume and wear it
* the King of Home Runs costume is unlocked for anyone that is FameStar level "Headliner" or above; you must go to the FameStar Rewards menu and then select the costume and wear it
* the 5,000,000 points is cumulative over all games, make sure to wear the King of Home Runs costume for at least 2,000,000 of it, to save time