Q: How many things I have to collect in Treviso Canals?
A: There are a total of 13 chests, 2 Lyrium chests and one Altar.

Q: When should I start progressing?
A: You can start as soon as you unlock Treviso Canals, however, I recommend you start after recruiting Taash, having "Bloodbath" (Lucanis') quest and "Statuary, Fine Art, And Antaam" side quest available.

Q: Why do I need to have Taash and these two quests available?
A: They are required for some of the chests, as one is locked behind Taash's ability to breath fire and the other two are locking some paths. It would be easier that way to collect everything in one go, but it's up to you how you approach this.

Please take in consideration that some of the chests (tied to the "Bloodbath" quest) will become unreachable (and will update the total count accordingly) if you decide to save Dock Town.

Location:

Solution:
The first chest can be found just outside of the Casino.
Take the zipline towards the market area and use the ledge as shown here.
Drop down and you will have access to the chest.

Location:
For this one, you will need to have "Bloodbath" quest acquired.

Solution:
Progress through that quest until you reach this location.
Go through the balcony and follow the path forward, up the stairs.
Go through this door.
You have reached the chest.

Location:
Go towards the southern area of the map in this location.

Solution:
Reach this well in The Drowned District.
Go through this door and follow the hallway path to the right.
Go right again through this hallway and up the ladder.
You've reached the chest.

Location:
Close to the previous chest, reach the area where a bunch of buildings are being submerged in the water.

Solution:
You will need to jump roofs around.
Use Spite's ability to pull structures from the fade to get across.
Jump another roof and drop down through the hole.
You've reached the chest.

Location:
Also close to the previous chest, go to this area that is controlled by Antaam.

Solution:
The chest is found inside a room.
Go left and open this door.
You've reached the chest.

Location:
The location is also next to the previous chest, although for this one you will require Taash to have been recruited.

Solution:
Vis-a-vis from the Antaam controlled area, go through this gate.
You will need to unlock this gate with the help of Taash.
Ask Taash (or use the dagger) to light up these braziers.
Go up the ladder next to the brazier and lit this next brazier.
Move across and light up these last two.
Now you have access to the chest.

Location:
From previous chest, there is a path to this location in the Streets of Coin Financials.

Solution:
Use Harding's ability to move rocks on these under the water.
Now you have a path to the chest.

Location:
From previous chest, move to this location.

Solution:
Use Spite's ability on this to get across and go to this room.
You've reached the chest.

Location:
Go to this area in Streets of Coin Financials.

Solution:
Open the highlighted door.
You now have access to the chest.

Location:
From previous chest, go to this location.

Solution:
Near the water there are some stones. Use Harding's ability on them and go to this door.
You've reached the chest.

Location:
From chest #9, go to this location.

Solution:
Cross the bridge and open this door.
Move forward and take a right.
Open the Lyrium door.
Take a right again and go through this door.
You've reached the chest.

Location:
If you're at the Casino, take the zipline that goes closer to the Market district and instead of going to the market, move straight forward from the zipline.

Solution:
Go up this ladder that's near the Beacon in Heart and Central.
Go across the roof top, not through the window.
Drop down and go through this corridor.
You've reached the chest.

Location:
For this chest, you are required to have acquired "Statuary, Fine Art, and Antaam" quest. Reach this location.

Solution:
Destroy the rubble blocking this door and go through it.
Open the Lyrium door.
You've reached the chest.

Location:
From Chest #12, go to the courtyard of Dellamorte Estates here.

Solution:
Take a right and you will find this Altar. Activate it.
The Wolf Spirit will be in this location under a roof.

Location:
Reach this location that is part of the "Bloodbath" quest, where Aquila usually is found.

Solution:
Go across the roof top.
Go through this window.
Interact with the library.
You have access to the Lyrium chest now.

Location:
From the Altar location, go to this area.

Solution:
In this location, you will need to rotate some statues to their correct angle.
You can use Spite's ability to know which angle each statue needs to be rotated, or copy the following placement.
After that, you will need to use these 3 levers. Use Spite's ability to open up the path to them.
Once that's done, you will have access to this statue that also needs to be rotated. Use Spite's ability or copy me.
You now have access to the chest found here (the statue will point its location as well).

Hope this guide was helpful and you've achieved Treviso Canals completion :)
Always open to feedback!