Hello, thank you for playing!
150 is the intended starting health, yes. :) The tutorial is meant to be unwinnable to show the player the difference between using the Retreat option or choosing to fight until the end, as well as to highlight more dangerous second half of battles. (Plus it gives an excuse to introduce the shop and give the player a proper fighting chance.)
If you consider finishing the first (non-tutorial) battle to be a completion of the game that's great! Since I didn't add an actual win condition or message of any sort. :D There enemies do get more difficult every time you win, up to five wins at which point I ran out of time to add more battles and enemies. Also, after two wins, better items go on sale in the shop, there are four tiers altogether (and a maximum team size of five.)