Complete Route. I made a mistake. I forgot to grab the key before I warped after beating the Pirate Dragon. You see me have to go all the way with Hawk Man to get it. Otherwise, this route is optimal I think. At least if you aren't getting the Tasmanian Sword. Speaking of that, I believe you skip 2 bosses if you use it and it would make the run more boring I think.
The only thing I'm still unsure of, as I mentioned before, is the Shogun gear. It certainly speeds up the Zombie Dragon fight which still takes ages. It takes like twice as long without though. I also think arrows would speed the Mummy Dragon fight up a lot. The problem is you can't really get the items you want in this game and picking up stuff takes forever. I guess if we could get 10 arrows without wasting too much time on the way to the Mummy Dragon, it might be worth it.
Oh, and I ended it at the last dungeon cause there's no point doing that cause it's so straight forward.