While Guthix Sleeps
Requirements : 43 Prayer, ability to kill a level 23. Possibly 85 Slayer.
Items Needed : Money
NPC : Sir Tiffy Cashien, Lanthus, Khazard Guard
Reward : None
To start, click the third teleport. It looks like this : Level 37 : Falador Teleport. Don't worry - 37 Mage is not needed, and it won't give you experience. Follow the path that goes east until you find a fork in the road, go left and talk to Sir Tiffy Cashien. Talk to him, say yes and he will tell you to get a Dragon Bitter, Abyssal Whip and a fighter hat.
For Fighter Hat : You will see a portal right next to him (West), and it's purple, but still visible. Click it. Turn protect Melee on via the prayer tab and kill 10 Khazard Guards. Each kill gives you 1 point, and you can check your points by Talking to Lanthus. When you have killed 10 Guards, turn your prayer off, Right Click Lanthus and "Trade Lanthus". The second item is a fighter hat. You have got one of the items of the quest.
For Dragon Bitter : Go to ::mall or ::shops and "Talk to Giles". The first item in the shop will be a Dragon Bitter for 1 GP.
For Abyssal Whip : You can get an Abyssal Whip the easy way, or the hard way.
Easy way : Go to ::mall or ::shops and "Trade Shopkeeper" and then buy an Abyssal Whip for 20 million GP.
Hard way : (85 Slayer needed) Go to ::home, and just outside the bank wall there will be a portal. Click it, and choose the last option, Slayer Tower. Run South till you're behind the wall, and attack an Abyssal Demon, and it will eventually drop an Abyssal Whip.
After you have got these 3 items, go back to Sir Tiffy Cashien and "Talk to Sir Tiffy Cashien". You will finish the quest.
CONGRATULATIONS ON FINISHING WHILE GUTHIX SLEEPS!