After Burner Climax

Play until you get to stage 5.

This game is not very difficult so getting to stage 5 shouldn't be that hard. Remember to use your climax power often since it's extremely powerful and recharges quickly. Missiles also tend to work better than guns so don't be shy about firing those off as well.

Achievements are not disabled when you enable EX cheats so you can turn those on as you unlock them.

Pretty self explatory. Simply Choose a plane and complete 5 levels in arcade mode. My opinion is to unlock all the EX Options first so that you can tweek the settings and gain alot of the other achievements in the process.
The most important I will say is the Continues. Just simply Keep dying until you see the Game Over Screen 10 times for unlimited continues!