Task 1: Finding Impaz
Catch up with Shad
Following your adventure in the Temple of Time, head back to Telma's bar. On the way, you'll get a letter from Renado regarding Ilia's memory. Once you get to the bar, Telma will tell you to find Shad in Kakariko Village. Once in Kakariko, if you haven't met up with the golden wolf in the graveyard yet, now would be an advisable time to do so and learn a new Hidden Skill.
Go into Renado's hut and engage him in a conversation. He will tell you that he thinks he knows how to get Ilia's memory back, but you will have to deliver a letter to Telma which explains the process first. Following the conversation, go into the basement and talk with Shad. Shad explains how the statue he is admiring is related to the Oocca, and that it may be a key to restoring Ilia's memory. Once you're done, head back to Telma's bar.
Give the letter to Telma, who exchanges it for the doctor's bar invoice. Locate the doctor's office at the west end of Castle Town's west avenue and deliver the invoice. The doctor, however, will not help you, as the only thing on his mind is why he can't pay the tab. Enter the north room in the doctor's office and push the wooden box to reveal a green stain. Transform into a wolf and sniff the medicine to learn its scent, then use your senses to track the scent through Castle Town.
The Wooden Statue
The medicine scent leads back to Telma's cat, who you will find outside of the bar. She admits that she stole the wooden statue from the doctor's office, but claims that it was taken from her by the Stalhounds in Hyrule Field south of Castle Town at night. Go out there to find them (it has to be night before they'll appear). A pack of Stalhounds will appear and attack you. Once you defeat all of them, you will receive the wooden statue.
Take the statue back to Kakariko Village and show it to Ilia. The statue will bring back a tiny portion of her memory, and the Gorons will recognize the carving came from the Hidden Village. Darbus will tell you to meet him at the village entrance, north of the Bridge of Eldin (it is marked on your map).
Once you get there, Darbus will smash through the landslide allowing you access to the village. He warns you about enemies in the village and that you should take them out before they see you. If you are running low on arrows, or have not gotten the Hawkeye, get them now before you head into Hidden Village. You might want to play the STAR minigame to earn a larger quiver as well.
Hidden Village is riddled with 20 Bulbin Archers. Before you proceed through the town, equip your bow with the Hawkeye and use it to take out as many enemies as you can. Be sure to look on the upper levels, through windows, and behind boxes. After you sweep through the town, check the back alleys to find any lingering enemies. The counter at the bottom-right of the screen will tell you how many you have left to defeat.
After you defeat all 20, the old woman Impaz will emerge from her home in the rear of the village. She explains how she met Ilia and will give you Ilia's charm, the key to returning Ilia's memory. Also, before you leave, howl at the howling stone to trigger a golden wolf appearance near Castle Town. You must leave the village to change into a wolf and then come back in to the rock.
Note that the Poe and Piece of Heart here cannot be obtained until you restore Ilia's memory completely.
Task 2: Fixing the Cannon
Back to Shad
Head back to Kakariko Village and give Ilia her charm. It will remind her of the times she spent with you, and her memory will return. She will give you the Horse Call and some important info about the Dominion Rod. Head back to Hidden Village (participating in the cat minigame to earn a piece of heart if you so wish) and show the Dominion Rod to Impaz. Seeing the Rod will convince her that you are worthy of receiving the Ancient Sky Book.
Go back to Renado's basement and show the book to Shad. He will set out to investigate some special symbols near statues, and indicate their locations on your map. Seek out the symbols. The magic in the book also restores your Dominion Rod to its former glory.
The First Symbol
The first statue is in the southern section of Eldin Province. Go to the north wall and climb up the ledge to find a statue. Use the Dominion Rod to pull the statue from its alcove and stand on the glowing symbol to learn part of a magic word.
The Second Symbol
You'll find the second statue at the north end of Eldin Bridge, along the east side. Use the rod to move the statue and learn the next symbol. While you are at it, you can grab a piece of heart.
The Third and Fourth Symbols
Head southeast from Castle Town's east exit. You'll find the third statue sitting on a pedestal in an amphitheater. Use the rod to move the statue between the stone ledge and the pedestal, then hop across it to get the symbol. You can also use the statue in a similar manner to get a treasure chest.
Another statue is in an alcove north of the Great Bridge of Hylia. Move the statue south and position it beneath the vines. Grapple up to the vines and drop down on the statue to access the alcove with the symbol. The statue will help you get the chest in the other alcove as well.
The Fifth Symbol
Travel west from the warp point in Gerudo Desert until you reach a set of irregularly shaped stone blocks. Lead the statue off its perch, then jump from the northwest block to the statue, and then to the block where the symbol is.
The Final Symbol
For the final symbol, head to Coro (the Lantern Oil guy in Faron Woods) and destroy the boulder northwest of his home, then move the statue to collect the final symbol.
After collecting the symbol, move the statue into the hole in front of the tree. Transform into a wolf and use Midna to jump over the wall to get to a chest containing a piece of heart on the other side.
Letter from Shad
At this point, warp to any open field zone (e.g. Kakariko Gorge or in front of Castle Town, which is a good location if you are ready to pick up the seventh hidden skill) and the postman will appear right away. If he doesn't appear, your did not get all of the symbols so go back and re-check under all of the owl statues.
You will get a letter titled "Update".
When all six symbols and the letter from Shad have been collected, return to Kakariko Village. Shad will read the magic word, which will allow you to move the statue with the Dominion Rod. Beyond the statue is an ancient cannon. Talk to Shad to get him to leave, then enlist Midna's aid to warp the cannon to Lake Hylia.
Once there, talk to Fyer. He will notice the cannon and offer to fix it for 300 rupees. Pay him and grapple into the cannon once it is completed to be blasted to the City in the Sky.