Here is the full list of all 30 Home Run Stars achievements worth 400 gamerscore.
Win a bronze score medal at the end of a Home Run League match.
Hit the Ferris Wheel in the Carnival.
Hit the Dragon's head in the Dragon's Den.
Hit the Pirate Ship in Buccaneer Bay.
Knock down 5 infield targets within the same game.
Erupt both volcanoes in Buccaneer Bay.
Battle Eric the Rookie in the Carnival and win.
Battle One Shoe Cam in the Carnival and win.
Battle Lucky Lee in the Carnival and win.
Reveal the treasure in Buccaneer Bay.
Win a silver score medal at the end of a Home Run League match.
Hit a 5X multiplier in the Carnival.
Complete an Avatar FameStar Challenge.
Unlock Buccaneer Bay stadium.
Unlock Dragon's Den stadium.
Battle Line Drive Angie in the Dragon's Den and win.
Battle Gorgeous Warner in the Dragon's Den and win.
Battle Pistol Pete in the Dragon's Den and win.
Win a Duel, Home Run Derby match and Home Run League match.
Hit a 5X multiplier in the Dragon's Den.
Find and hit the moving gold treasure trophy in Buccaneer Bay.
Win a gold score medal at the end of a Home Run League match.
Hit 5 consecutive balls in Home Run League Mode
Complete Home Run League Mode.
Battle Cash Money in Buccaneer Bay and win.
Battle Fireball Terry in Buccaneer Bay and win.
Battle Cyclone Williams in Buccaneer Bay and win.
Win a gold score medal for every match.
Score 500,000 points in a Home Run League mode game.
Complete all the Avatar FameStar bonus challenges