Once you figure out the strategy for each part in the level it becomes pretty easy to master the moves you need to do to advance further. It becomes especially easy once you get the Tiger attack and can pretty much just decimate enemies and bosses from that point forward. With the doubled Tiger attack, you don't even have to move for the last boss. Add in a pretty liberal amount of health containers and even with mistakes you should be able to work your way through the game with the 3 continues. Using the "Backup" option, which essentially save states where you last had a game over, gives you unlimited continues, but you really shouldn't even need it.
Cool thing I found is that when you do use the "Backup" option after you finish the game, you start again on the first level but retain all of your Tiger/life powerups, which makes the first few levels especially fun since you can just plow through unscathed. Not sure if the ending is any different after that, but I guess it wouldn't be too difficult to find out!