Well, therein might be the problem. I've actually yet to play any of the Turbo Ys games. My introduction to the series was Ys for the Sega Master System. I'm actually not sure how to even defeat the first boss since half the room he's in is covered in fire that is an almost instant kill if you touch it and all he does is teleport on top of this fire. The first boss in Ys IV is similar (I played an emu version of the SFC one) in that he teleports around the room while flames shoot out of the walls which will generally instant-kill you (or at least knock your health so far down you can forget about winning the battle). I don't consider myself a complete n00b when it comes to action-RPGs, but after having my ass handed to me twenty times apiece, I gave up on both bosses and both games.
You know, as long as you're powerful enough to damage the boss, you can beat him without taking a single hit of damage from the flames. The main issue with Ys SMS is leveling high enough to be allowed to damage a boss, even though they can all be beat without taking any damage by proper dodging/attacking.
Ys I & II PCE is completely different. Ys I in particular has been dumbed down to be super noob-friendly and extremely short.
If you try either Ys again, you should grab the Golden Vase from the pond in the field, sell it at the pawn shop, buy the ring and give it to the guy in the bar then buy (if I remember correctly) the second cheapest sword and shield and armor. Then go talk to Sara(?) to get the crystal.
In a few minutes you'll go up a couple levels or more and have a good set of equipment without fighting a single enemy. You could probably already damage the first boss in the PCE version, but might need to go up a level in the SMS version. But it'll be easier to level up since you can fight tougher enemies (thieves around the shrine?) with your better sword and gained levels.