I would personally love to see a Clash at Demonhead run. However I really don't have the skill or patience to do it myself. But having recently played through it I have come up with a few things to give someone who attempts it a headstart.
First of all an image of the map, with all the routes labeled and a key of all the significant people/items/bosses that are on certain routes:
http://www.rpgclassics.com/~onlinelife/images/DemonheadMap.png
Your main goal in the game is to get the Six Medallions, Four of them can be gotten from bosses without any story pre-text. Just find their fortresses and beat them. Those Bosses are Gahz on Route 11, Max on Route 7, Mush on Route 16, and Shark on Route 28.
To get the Fifth Medallion you have to handle a bit of a sidequest. When you reach Route 3 you first meet Michael, then on Route 17 you meet the Fairy Faysha who opens the way to the Hermit on Route 35, from the Waterfall on Route 6. Defeat Rowdy to save the Hermit. Later you meet Michael again on Route 15 and he tells you to get the Magic Stone on Route 27, you see him again on that route. When you get the Stone and return to Route 15, enter the second well and Michael will be down there. Placing the stone in the door opens the way to the first boss fight with the Demon. You HAVE to lose this battle, it may not look good for a Time Attack to get a Game Over but it has to be done. From there re-enter Route 15 then take the Shortcut to the desert Route 33 and Enter Guycot's Fortress, and meet Faysha again who tells you to go to the Hermit. Return to Route 35 and the Hermit will tell you to get the Sword of Apollo on Route 40. Once you have that, go to Route 39 and use the sword during the second fight with the Demon to get the Fifth Medallion. One hell of a run-around for a Medallion eh?
And for the sixth and final Medallion, first you must face Bopper on Route 21. After defeating him once he flees and you have to face him again on Route 42.
Once all that is done the way to the final battle is open. Saying all that now, there are a few things to consider.
Pandar is an optional boss, not needed to beat the game, and thus should be skipped. This saves you the trouble of going down Route 31. I don't know the game well enough to say whether or not you must talk with Joe. I've never finsihed it without talking to him. If you cna skip that, it'll save you the trouble of going to the end of Route 32 and backtracking. In fact if you don't fight Pandar or meet Joe you can skip going in that entire area of the map.
You start the game with a Shop Call, so you don't actually need to go to Route 5, just make sure you have enough cash to buy another Shop Call whenever you use the first one. But going to Route 5 may be worth it for the regenerating Gold. It takes awhile to get to it, but if you spend just enough time getting gold bars you could make a fortune on Route 22. It's worth noting that Bang moves much faster using the Jet Pack and the Boots. However you can only carry three of them at once, and they each cost quite a bit. So building up enough money is advantageous, but it may be possible to manipulate luck to get the enemies to drop what you need. If you do that then you can skip Route 5 entirely.
You only ever need to use the Hermit's Force Power once, to escape from Route 35 you need to use the First one. This saves some time on manipulating the menus, however the second Force Power, Teleportation would be invaluable in a Time attack. You need to get Bang's Force Level up to 200 to learn it, and it costs 60 Force Points to use. But you can warp to any Route (or rather, any Map 'Node' that the routes are connected to) you've been to. Considering that some of the objectives are so far apart, even an efficient route plan could be shortened considerably with Teleportation.
One of the bosses, Shark, is fought underwater. When underwater Bang's health slowly goes down unless he has an Aqualung equipped. If you're fast enough you should be able to beat Shark without it. The other places in the game where you need an Aqualung are also fairly short, and far apart, thus if you have Bang's health up to full when he dives under and avoid the enemies underwater (in a Timeattack that shouldn't be an issue) then you may not need to buy one at all.
You do, however, need at least one SuperSuit. To get the Magic Stone you must dive under the lava in Route 27. It is the only place in the game you need a Super Suit, so remove it as soon as you're finished lava-swimming. You walk much slower wearing one of those.
When you come back from the Hermit on Rotue 35 you emerge on Route 8. If you have a JetPack or Boots you can take the 'upper' exit from Route 8 to get to Route 7. If you do the first part of the Hermit quest right away at the start you could then face Max on your way back.
Overall, I think the best Route to take is:
1 (you start here, don't take too long facing Guycot), 3 (meet Michael then turn around and leave), 2, 11 (beat Gahz), 9, 12, 17 (meet Faysha and turn around and leave), 14, 6 (entering Route 6 from 14 pretty much puts you on top of the shortcut to the Hermit's Den), 35 (beat Rowdy, meet Hermit, get Force), 8, 7 (beat Max), 8, 4, 1, 3, 12, 20, 15 (meet Michael), 18, 16 (beat Mush), 27 (get Magic Stone, turn around and leave) 16, 19, 28 (beat Shark, turn around and leave), 19, 18, 15 (open door, fight Demon, die), 15 (re-enter and take shortcut to desert), 33 (meet dying Guycot, meet Faysha, then take shortcut back to 15), 20, 14, 6 (shortcut to Hermit's Den), 35 (talk to Hermit about Demon), 8, 4, 1, 3, 12, 20, 18, 16, 27, 37, 40 (get Sword of Apollo, turn around and leave), 37, 27, 16, 18, 15 (take Desert Shortcut to 33), 39 (beat Demon and emerge on Route 38), 30, 21 (fight Bopper), 42 (fight Bopper the second time) 43 (finish game)
Now that's quite a lot, and notice it's a warpless run. Yeah it's all from one point to the other, but I believe it's the 'best' route to take. However if you use Teleportation to warp around you can shorten it significantly. While it's all going to depend on how much Force you build up (and how fast you can do it), I believe the best places to warp are after you get the Magic Stone warp back to route 15 (take the other exit, not the way you came in Rotue 27!), after you meet Guycot and Faysha on Route 33 you warp right to Route 6 to get to Route 35 (you can't warp straight there, unfortunately), and from there Warp right to Route 37 then on to 40 (If you're going to do that, the when you're in Route 27 getting the Stone, don't turn around and leave. Instead keep going and take the other exit so you can 'activate' that node for Teleportation, as I mentioned before.) Then either Warp back to Route 15, or to Route 33 (you'll have to make sure to enter Route 39 if you're going to do that, as if you just warp out of Route 33 the first time around you can't warp back unless one of the 'nodes' are activated). So that means to make the best use of Teleportation you should use it those four times to shave off quite a lot of time. That means you have to have at least 240 Force Points, 200 to get Teleportation and 60 each time you use it.
You need to buy at least one Super Suit for the Lava, and that's all you HAVE to buy in the game. But as I said before, the Boots and Jet Pack make Bang move much much faster and it would be wise to make use of that. But I cant' really predict what routes those items would be best used on. And keep in mind that a bit of time is wasted summoning the Shop and buying everything (the slow text speed and chatty shopkeeper don't help matters)
I hope all this info will help someone time-attack this awesome game. For more detailed info on specific parts of the game check out the walkthroughs for it at GameFAQs.
(EDIT: Oh, one big thing I forgot to mention. I didn't overlook Route 13, the reason why I never included that in my Route-plan is because it's essentially one-way. You can only go from the North exit to the South exit in that route, so unfortunately you can't quickly get to Shark right after beating Max)
(EDIT EDIT: I fixed the link to the image, I can't believe I misspelled head.)
