Hmmm. Haven't played this in forever, but I'm pretty sure there's no way of continuing. I never knew of one. 2 had the codes for continuing, and 3 gave you the continue for making it to Egypt, IIRC, but I'm pretty sure you're one and done on this one.
This is a game that I haven't played in some time. I know when I did play it regularly, I could make it to the end boss, at which point I would usually get owned. Even though I can't tell you off the top of my head which new techniques you get at which heart levels, the biggest tip I can think of right off would be to try to get those hearts as early as possible.
Learning to take a lot of the earlier enemies out with straight punches (if you aren't already) will help with that. If you notice yourself getting low on life, then just focus more on finishing the mission. It definitely takes some practice at any rate. Good luck and have fun!