I found it easiest to do this on a second play-through as you should understand the locations, item placement, shooting/melee mechanics, boss encounters, etc. much better. Complete the game on normal or easy on the 1st play-through and you will get the Albert-01R on your 2nd play-through, which is an extremely powerful hand gun, especially on easy mode. With enhanced handgun ammo you can one-shot head kill almost all molded, and quickly dismantle bosses. By only needing basic ingredients like gunpowder and strong chem fluid, you will be able to run right through most situations. Also the double-barrel shotgun is a great gun, but I didn't even bother with the grenade launcher or flamethrower. The less bulky items in your inventory, the better.
There are hundreds of speed run videos online but keep in mind for your 2nd play-through you likely will not have infinite ammo, since this is unlocked via completing Madhouse difficulty. Use a guide where they actually pick up ammo. You can beat the game in under 4 hours pretty easily and also grab some other achievements on the way.
Use this video:
Good luck!