General Advice
Character Choice: Pick Warrior or Amazon as your character always. They are the only ones with the Orientation skill, which lets you see the entire map of every land and dungeon. This will allow you to instantly know which quests a land will have, where the dungeons are, and let you identify key rooms and find staircases much quicker in dungeons. No other character has anything that competes with this. If you're playing with two characters I suggest making your second a sorceress, as the lycanthropy power increases your movement speed significantly which is obviously very powerful in a speedrun. Werewolves are also very powerful in the early game.
Skills: As mentioned before Orientation is a must have, you should buy this skill before you even leave town after starting the game. Concentration is incredibly cost effective in the early levels, giving you +5 to Strength and Dexterity per level. This makes you hit harder, more consistently, and increases your AC. Master of Arms is a strong 3rd place, passively increasing your attack speed and chance to hit. You are going to need Concentration level 2 to wield Njolner.
Berserker: Maximize your chance of finding a berserker tome early. This spell is borderline necessary for killing enemies in a timely manner, which is something you're going to need to do a lot. Typically if I don't get berserker before I start level 5 I just reset the run because it's THAT important. Explore the early levels even after finding staircases to look for lecterns. If you don't find berserker before finishing level 4 you can go back to town and check Elmeric's shop, if you've gotten a few other spell tomes you may have enough money to buy a berserker tome but it may not even be in his stock.
Strength vs Vitality: Your objective with distributing your stat points is to put as many points into strength as you can manage. Higher strength = things die faster. Draak is also a dps-check, meaning you need to reach a certain level of damage output before it becomes possible to kill him and finish the game. Eventually you are going to have to put points in vitality or enemies and traps will start one-shotting you. You should try leveling up your vitality at some point in the midgame and it's generally advisable to do so after you get a weapon upgrade, since you can expect the weapon's raw damage to carry your DPS for a few levels. For the final fight you'll want to have somewhere around 50 vitality. This is the point where Draak stops killing you in two hits, anything less than this and you run the risk of needing more health potions than you can carry. It is theoretically possible to finish the fight with something like 30 vitality or perhaps less, and it might even be a few seconds faster, but it is extremely risky.
Economy: Gold is a crucial resource. It will allow you to buy potions, scrolls, and skills, all of which are necessary to run the game effectively. Generally speaking, you do not need a lot of gold in order to beat the game. Aside from the 1st level of Orientation, health potions, mana potions, and magic door scrolls, everything else is optional. You should generally avoid killing enemies or looting containers for the express purpose of farming gold as the payoff is not usually worth the time commitment unless you're finding it hard to keep stocked up on the essentials (health potions and magic door scrolls). When you find yourself with extra gold you should be buying haste/teleportation/invisibility scrolls. I have experimented with all three of these options and I find teleportation to be the most cost effective. Teleportation will let you bypass chokepoints that normally would require you fight or lure multiple enemies, skip steps in certain quests, and just generally help you out of tight spots. I also try to buy a couple invisibility scrolls for level 29 as enemies in these levels are extremely strong and there are a lot of tight corridors to get stuck in. I buy a new sword after level 8 unless I have the disciples sword from the sun cross quest, and then I keep that sword for the rest of the run. Obviously if I get the sword of elwon or the celestial sword I keep those as upgrades, and sometimes I'll also kill the optional boss in Horgan's Amulet quest for his sword/exp if I feel particularly weak at that point in the run.
Magic Door: This is your biggest boon when it comes to back-tracking, which you'll find yourself doing a lot. This spell allows you to create a door that will allow you to return to town, and then return to wherever the door was placed. Generally you throw this down anywhere you're going to have to come back to, and then once you're ready to return you can use the "Restart in Town" option in the pause menu to teleport back to town from anywhere. Restarting in Town will drop all of your non-quest related equipment on the ground, but if you manually place these items in your inventory before clicking it you will be able to keep them. Scrolls cost 1,000 gold each and the book costs 38,000. Since you'll only need to cast this 10-15 times throughout the run you should never buy the book. It's usually even worth it to sell the book if you find it and just buy scrolls. Elmeric will always have scrolls in stock.
Quests
I won't be going over all the quests in incredible detail, if you want specific quest guides there's a good source here. I'll be going over what steps can be skipped, and what the benefits and drawbacks of each quest are.
Town
On game start I sell my shield which gives me just enough gold to buy a magic door scroll, a health potion, and the orientation skill. Then leave town, use orientation, and bring up the map.
1-4
The Sun Cross: This is the best quest you can get as it will give you crazy EXP and can be as fast as the witch. Place your magic door at the Antique Dealer's, or as close as you can while running to level 1. Go into the dungeon and focus on finding berserker, if you don't find it before the combat section of the quest you might as well reset the run. Once you have berserker, go to level 4, do the trials, take the sword and amulet back to level 3. Personally I take the fake cross and kill everyone in the monastery before getting the real cross. This is technically unnecessary but the experience values of the enemies are super inflated and will allow you to get a lot of early levels, so it is worth doing IMO. Once you get the cross restart in town and take your portal to Drakus.
The Horn of Plenty: Personally I just reset the run when I see this quest as it is the longest of the 1-4 quests by a large margin, gives very little experience, and is just annoying. It is possible to have good runs with this quest but since I've only committed like 2 minutes to the run at this point I don't see a problem with resetting. I have no advice.
Mika the Witch: Place your magic door at the Witch's house, or close to it. The real mirror is on level 2, the cursed mirror is on 4. Try to find berserker. If you didn't find berserker but have a few books you should at least go back to town and check Elmeric's shop before resetting.
5-8
The Unicorn: Magic door next to the unicorn, talk to the fairy, take her to level 8 and get the key, restart in town, take the door back to the unicorn. Easy quest, killing the druid will net you a lot of experience. Generally I reset after looking at Ardyl's map unless I see Unicorn or Sun Cross (Ideally both) as you will be underlevelled for the first half of the run unless you get one of these two quests.
The Reeds: Don't assemble the flute, just go down to floor 8 and kill the first 3 snakes on the boat. Then save the game, open the door, and kite the snakes around while grabbing the crystal. This is really difficult and will take some practice to get right. Another option is killing all of the snakes in the crystal room but that obviously takes more time, but you will get experience and some gold out of it.
The Antidote: Literally just reset
9-12
The Eye of Ra: I'm sure it hurts to reset your run once you've come all this way, but I am pretty sure this is the longest quest in the game by a large margin. It's just not worth it. You're going to have to reset.
The Hives: Find Rosso, get the sword, kill the queen. You can get the armour of fear if you feel like you need some extra gold, as it sells for a lot. This quest is pretty fast but is also very difficult and will take some practice. SAVE OFTEN.
The Burnt Out Village: Ideal quest for this slot. You don't even need to talk to the woman in the village; just put your magic door down next to her and run straight to the dungeon. Give the guy outside a health potion to get a free invisibility scroll, invisibility is great for traversing dungeons especially at later levels, I would hold onto it for now. The first floor is always the same, turn left at the crossroads to get to the first staircase. Then just rush to floor 12 and grab the baby. As soon as you have the baby in your inventory you can pause and restart in town.
13-16
Poison Vats: You can skip basically everything in this quest, run straight to floor 16 and dump 3 antidote potions in the vats, then grab the crystal. There is a decent weapon you can get if you do everything else in the quest, but it takes several minutes and is not really worth doing.
The Celestial Sword: This quest can be annoying and has some back-tracking. Put a magic door next to the entrance to the celestial sword in the land of Marghor, then go to floor 13, get the symbol from the prisoner in the chicken room, restart in town, go through your magic door, use symbol on rock, grab the celestial sword, put another magic door next to Shadire (or as close as you can while running back to the dungeon). Now, go back to floor 13 and destroy all the eggs in the incubation room, restart in town, magic door, talk to shadire. Put a magic door as close to the entrace to Omar as you can, go back to floor 13, then run straight to floor 16, put the celestial dagger on the pedestal and grab the crystal.
Horgan's Amulet: This quest is only slightly more straightforward and still quite slow. You can take the crystal without fighting the final champion, but if you fight him he will drop a fairly decent weapon. Your call.
17-20
Fountains of Immortality: The only thing you need to do for this quest is run to the last level and fight the boss. However, I like to stop at at least one fountain to grab an elixir of youth. These sell for 33,000 gold and take maybe 10-15 seconds to grab. Selling one of these will support your economy for the rest of the run.
Princess Jasmine: Buy some teleport scrolls and you can skip this entire quest. Just go to level 20 and teleport past all the traps.
Kolos: You have to kill the druid to get the vial of spirits. Make sure to grab all the books as well, they will sell for a fair amount.
21-24
The Three Gems of Hell: Can't really skip anything in this quest, nothing much to say about it.
The Pyramids of Light: This is an automatic reset for me. If you're on a great run feel free to try this quest but it requires so much backtracking and is so slow that I just give up on runs when I see the circles of life in Omar.
Trial of the Damned: The fastest quest in this slot, but still fairly slow. No skips that I know of.
25-28
Luxorious the Vampire: Arguably the slowest quest you can get here, statues can be slower with bad RNG. Requires running through a long predetermined level 25 to get a rock hammer, then backtracking to Serkesh to get the sceptre. After this you can run straight to the last level and just kill Luxorious for the crystal.
Statues of Arkhang: Fairly slow. You should place your magic door in the crystal room. You can destroy the statues with any ranged weapon so if you find the staircase before finding the wounded monk you might consider just buying a low-level bow to save some time. The monks on level 28 will take a few seconds to attack you after you destroy the statue, if you restart in town before they attack you this will break the quest and not allow you to collect the crystal.
The Holy Number: You can just walk straight to floor 28 and set the number to 540.
Draak
The final floor is always the same layout. Grab Njolner* if you don't already have a good weapon and then head straight to Draak. Place a magic door before starting the fight, head back to town and fill your inventory with health potions. Then you'll have to lure Draak away from his wyverns, either by getting him stuck on one of the walls just outside his room, or lure him to the point that the wyverns are no longer rendered in. The second option requires you kill the last two groups of wyverns leading up to Draak, but is more consistent. Save before you start killing him, pop the time orb around 50% health, then take the astral hand back to town and use it on the pillar.
*Remember that Njolner has a 20 dexterity requirement. As warrior's base dexterity is 10 you will need to either have put 10 skill points into dexterity or have level 2 of the concentration skill. You can use the boost from concentration to equip the weapon.