Here is the full list of all 12 The Simpsons Arcade Game trophies - there are 7 bronze, 4 silver and 1 gold.
Complete the game on Expert difficulty in individual Quarters mode.
Complete the game four times, once with each character.
Complete the game in 30 minutes or less.
Playing from stage 1, get Bongo to appear in 4 different levels.
From stage 1, make it to the stage 3 bosses in Survival Mode with the Japanese ROM.
While performing a Team Attack, damage 25 enemies.
Defeat the Wrestler without any player dying.
Earn 250 points (US) or 25,000 points (Japan) in a game.
Hurt Smithers with one of his own bombs.
Playing from stage 1, defeat the battling robot.
Play in a 4-player match with three other people.
Playing from stage 1, fall through the deck after Smithers.