Adopt a Zig

Reward: possibility to purchase a Zig or more, for 70 Elyps each.
Total cost: 77 Elyps (7 for plushie, 70 for the Zig)
Time to complete: approximately one hour.

Go to Jungle, at the border of Void & Maiden Grove, at the Shadow Runners camp.
Target the stable boy, Mac'Roffy Shillan, and buy a plushy for 7 Elyps.
Use the Rywards to equip the plushy:
Open the Encyclopedia by clicking on Shift + E or E.
Click on:
Rywards
Supply Box
Teddies
Plushie Gubani: click on "Run".

Talk to O’Ronin Dalin.

Target the elements whose position is indicated on the map and start the ritual tasks.
When you click on: “I don't understand what to do” and then on the question mark showing the Encyclopedia. The text appears:

“You can remove from your character's hand any object present in your supply box thanks to the action icon (1).
Some objects allow you to perform one or more other actions (2), some of which will require you to target an element present on Atys.”
Click on all the items shown on your screen. After reading all, you will be rewarded with 10 Elyps.

On your lower right corner, several icons appear:
Rite - Feeding - Exercising - Washing - Draining - Remove

Your map will show for each of the 4 continents a location relevant to the rite:

Feeding:
Find a suvue on the Witherings map and target it.
When ready, click here to launch the ritual task.

Go to the Jungle, near Zora, above Still Waters, as indicated on the map.
Target the suvue, then on the icon "Feeding” on the lower right corner and the text appears:
“You take a suvue leaf and make your gubani plush eat. Sure, it's only a stuffed animal... but it seems to like it. Really! “
Click on “OK”.

In the encyclopedia, it shows “You have completed a ritual task”: ¼

Exercising:
Find the "Flame of honor” on the Burning Desert map and target it.
When ready, click here to launch the ritual task.

Go to the Desert, near Pyr, as indicated on the map.

Target the flame, then on the “Exercising” icon on the lower right corner and the text appears:
“You're at the starting point of the Zigs fitness trail.
This course has been designed to get your Zigs back into peak physical condition.
Go to the various points on the course, which will be displayed in the mission and on the map.”

Then a flag shows on the map and a target is added to the compass. Run to the location.

The 3rd target is back to the flame, where the text appears:
“What a pleasure to see you both frolicking in the hot desert sawdust.
Look how happy the guibani plush is, he's happy to have run into mommy's arms.”

In the encyclopedia, it shows “You have completed a ritual task”: 2/4

Washing:
Find a water effect on the Aeden Aqueous map and target it.
When ready, click here to launch the ritual task.

Go to the Lakes, near Fairheaven, as indicated on the map.
Click on the water, your target will indicate “Water Source”.

Click on the “Washing” icon on the lower right corner and the text appears:
“What a joy to take a dip with your lovely plushie.
Wait... the fluffy one there... it swells! Take it out the water quickly...”
Click on “Ok".

In the encyclopedia, it shows “You have completed a ritual task”: 3/4

Draining:
Find a nice draining place for your plushie on the Verdant Heights map and target it.
When ready, click here to launch the ritual task.

Go to the Forest, near Yrkanis, as indicated on the map.
Walk around the pile of fertilizer and keep clicking until you find a targetable location.
It can take a while to be successful. I first had it targeted, then it disappeared. And it took quite a while before I could target it again.
Perhaps you can only target during the night, or certain weather conditions?

Your target will indicate “Fertilizer”.
Click on the “Draining” icon on the lower right corner and the text appears:

“Well... we won't dwell on it...
However, the ecological gesture is appreciated, and then... the florists are happy too. All is right!"
Click on “Ok".

In the encyclopedia, it shows “You have completed a ritual task”: 4/4

Click on the last remaining step on the encyclopedia.
A mission (as well as a compass target and flag on your map) will be added to your journal:
Talk to O’Ronin Dalin.

Return to the Jungle, at the border of Void & Maiden Grove, at the Shadow Runners camp.
Target O’Ronin Dalin, and click on "Hello".
O’Ronin Dalin says:
“Oh Bravo!
I can see that you have done very well. You will undoubtedly be among the best parents for your future zig.
I am giving you access to adoption now!”
Click on “Ok".

Click on the last item on the encyclopedia. The following text appears:
"You obtain:
Unlock “Adopt a Zig” option from The Shadow Runners stable boy.
Click on "Close”.

A mission is added:
Talk to Mac’Roffy Shillian.

At the stable boy (a few steps further) you can buy a zig for 70 Elyps.