Use a cannon. The cannon will regularly hit 300s or more on the bosses. You will need to bring a DDS (dragon dagger poisoned++ and a whip as well (if you have high melee stats). Set up the cannon and turn it on before waking him. Wake him up and use the DDS special attack on him. Switch to the whip and continue to kill him. Bring mantarays (or the best food you have) as well as about 2 prayer potions (4 dosage) depending on your prayer level. I don't think there are any safe spots.
If you can't use a DDS and a whip, just use the best ranging or magic equipment you can get. Personally I found using magic on the Desert Treasure bosses much better than melee, even with much higher melee skills than magic (I believe it was not much higher than 60 at the time).