As soon as you clear the game once. The Extra Stage will become available in the "Extra Mode" menu.
Pick your best character/ship along with game mode -> Skill Card -> Difficulty.
Setting it on Novice is suggested. Note that regardless of the difficulty selected, the game will automatically have its rank level to 255. Its a short stage that will have various enemies shooting plently of bullets that you can counter back.
The Extra Stage boss is "Genocide Angel". Basically a powered up version of Bullet Angel with similar attack patterns as its original, but sparsed with more attacks and its faster. Like the original, it has a temporary barrier that activates if you initiate break mode, but it'll go away after a couple seconds. Same strategies apply to Bullet Angel from the normal game and Mission Mode. But with more concentrated attack fire to evade and counter with.