A 1UP is awarded when any team (1, 2, 3, or 4 player) reaches 100,000,000 points. It is awarded in the form of an icon ship, an enemy ship, which you must destroy to make it release the 1UP icon. Only the player who collects the 1UP icon will unlock the trophy.
As with most trophies in this game, this is easiest to do in DUAL PLAY mode (controlling two fighters at the same time) or in multiplayer or both, due to the higher scores. Some players will find DUAL PLAY too hard, however playing DUAL PLAY by yourself essentially emulates a 2-player game and lends you the ability to revive yourself (as long as one of your fighters stays alive for 10 seconds).