Here is the full list of all 10 Gun Crazy achievements.
Beat stage one without using a power up.
You don't want this one!
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Beat the game without taking damage.
Beat the game without using a continue.
Beat the game without dying.
Beat stage one without dying!
Beat stage two without using a continue (at all).
Beat stage three without using a continue (at all).
Beat stage four without using a continue (on this stage).