When I routed this, I was surprised that arriving to Castle Shadowgate with the minimum items sends you down to the end instead of through the castle - therefore eliminating the need need for any other items/quests to finish the game.

• Bucket (Dungeon, Erik's Cell)
• Keys (Dungeon, Erik's Cell)
• Paddle Ball (Dungeon, Old Man's Cell)
• Quartz (Cavern)
• Feather (Town, Dock)
• Gold Coin (Various / Town, Old Lady's House) - only needed for purchasing Piranha
• Piranha (Town, Pet Shop)
• Coal (Highland Plateaus, Engine Room)