To All The Squirrels I've BEEN Before

When doing the Time Rifts at the top of each hour there will be orbs that offer various buffs similar to Cobalt Assembly or Torghast. One of the buffs is something like "Fluffier Fur" and says it makes you 100% more cuddly. Pick that option if you get it, and return to Soridormi. She'll have a dialogue option asking if she can pet you. Click yes and you'll get the achieve.

The hard part for me was to get a Titan Invader's Time Rift and not actually the buff, but here goes:

1. when you open your in game map (and while a Time Rift is going on) hover over the Time Rift icon and make sure it says "Titan Invaders" for this achievement to be possible.
2. when Titan Invaders is up: in phase 1 you can fly around and find medium sized yellow spheres on the ground and all you gotta do is repeat that until it offers you the Fluffier Fur option. But If people haven't been killing mobs, these spheres have not to dropped yet, in that case you need to kill the large Titan Keepers (Freya) for them to drop.
3. When you get the Fluffier Fur buff fly directly to Sidormi, talk to her and select the text "Yes" when she asks to pet you.
(it seems that choosing "Please don't pet me" option also counts for the achievement but personally, I didn't risk it)

As a Pandaren I was very offended that Soridormi didn't find my own natural fur appealing.