Arcade mode is unlocked after completing the final mission: Game Over.
You get to select a mission and play it from start to finish with 3 lives and a limited amount of time.
You play the whole game from "Crew Expendable" to "Mile High Club" with no cutscene missions and see how far you get, lives carry over between missions. You can pause the game but if you lose all your lives then you have to start over.
If you lose, the final score is just your score times the difficulty (1 for recruit, 4 for veteran).
If you win then your final score is your score, plus the time you took in seconds times 5, plus 1000 for each life, times two if you did not die and finally times the difficulty(1 to 4).
FinalScore = BaseScore + (Time * 5) + (Lives * 1000) * 2(Flawless) * Difficulty