Pretty easy achievement since you will have unlimited continues and can play on practice mode where enemies do not shoot (but they can crash into you and kill you).
First click on Raider Fighters 1 (you have an option for Raiden Fighters Jet, Raiden Fighters 1, and Raiden Fighters 2. Then click on Arcade and input the following settings.
Game Start: 1P Start
Stage Type: Fixed 1-2-3-4-5
Game Mode: Boss Rush
Difficulty: Practice
Medal: On
Credits: Free Play
Now you will go through each of the boss battles. Just be on the lookout for fighter jet/obstacles which can crash into you and kill you. If you die and run out of lives just press continue and you’ll get more lives.