Tiara mould, any pickaxe—mine the silver ore from the Rellekka mine located on the east side of Rellekka, a few steps north east of the agility shortcut (an iron pickaxe can be obtained from north of the Rellekka mine). Superheating will not work; click 'Smelt Furnace' rather than using the ore on the furnace (you will get a blue stage update notification), and then use the silver bar on the furnace again with the mould in your inventory to craft the tiara. Otherwise, the task will NOT be completed.
Pet rock. Enter your house in non-building mode; then, use your pet rock on a pet house. Then, you must retrieve the pet rock off the ground (by left-clicking it). Taking it from the "stored pets" interface on the pet house will not complete the diary task.
Combat equipment to kill the God Wars Dungeon generals, high strongly recommended. Boosts cannot be used. You must deal the most damage to the boss in order for the kill to count. See each individual pages for recommended gear/setups.