By completing missions on various difficulty settings in Story Mode, you'll be able to unlock and replay them in Stage Attack Mode.

Stage	How to unlock
Easy Stage 1: Tokyo	Beat Stage 1 on Easy in Story Mode.
Easy Stage 2: Kagoshima	Beat Stage 2 on Easy in Story Mode.
Easy Stage 3: Osaka	Beat Stage 3 on Easy in Story Mode.
Easy Stage 4: Hokkaido	Beat Stage 4 on Easy in Story Mode.
Easy Stage 5: Over New Japan	Beat Stage 5 on Easy in Story Mode.
Hard Stage 1: Tokyo	Beat Stage 1 on Hard in Story Mode.
Hard Stage 2: Kagoshima	Beat Stage 2 on Hard in Story Mode.
Hard Stage 3: Osaka	Beat Stage 3 on Hard in Story Mode.
Hard Stage 4: Hokkaido	Beat Stage 4 on Hard in Story Mode.
Hard Stage 5: Over New Japan	Beat Stage 5 on Hard in Story Mode.
Normal Stage 1: Tokyo	Beat Stage 1 on Normal in Story Mode.
Normal Stage 2: Kagoshima	Beat Stage 2 on Normal in Story Mode.
Normal Stage 3: Osaka	Beat Stage 3 on Normal in Story Mode.
Normal Stage 4: Hokkaido	Beat Stage 4 on Normal in Story Mode.
Normal Stage 5: Over New Japan	Beat Stage 5 on Normal in Story Mode.