Even though you have an unlimited amount of lives, all of the things done before that will not count after you die: try not to die while fighting the Boss.
Dungeon Mission
During Mission 5 the dungeon card. Once you complete mission 5, go to the mission select screen and to the top left there should be an extra mission called dungeon.
Prisoner Cards
Every time you rescue ten prisoners, you will get a card.
Solider Cards
You will get soldier cards when you kill 100, 200, 300, and 999 soldiers, for a total of four cards.
Type R Card
There is a card in the beginning of mission 4 called Type R. If you equip the card, your Metal Slug turns yellow and the gun moves in reverse. For example, if you are moving forward your gun will point in the opposite direction.
Collecting Card And Kills...