Just did this on 2022-03-27, Version 1.18.12, on a Random Seed. I did it using one World and one Wolf, I made Copies of the World in the Game's Menu.
Wolves
According to the Wiki (
https://minecraft.fandom.com/wiki/Wolf#Spawning), at this time; Wolves can spawn
"naturally above grass blocks, dirt, coarse dirt or podzol. They spawn in packs of 4, where 10% spawn as pups. They can spawn in these Biomes
- Forests
- Taigas
- Groves
- Old Growth Taigas
- Snowy Taigas
- Along with all variants of these Biomes (with the exception of Flower Forests)
My Method
I did this on Easy Difficult, on a Random Seed generated in 1.18.12, specifically, 460367020.
I went to
https://www.chunkbase.com/apps/biome-finder this website has some incredibly useful programs for Minecraft. This one in particular allows you to input your Seed, select the version the Seed was generated on, and analyze the Map. You can even input particular Coordinates (useful for marking your location on the Map in relation to other things).
So, I went and selected Bedrock 1.18, entered my Seed, then Filtered to highlight all the Biomes listed above. The closest was a large group of Forests. I went to the nearest applicable Biome, got 10 Bones, and found a Wolf.
- After getting 5-10 Bones, and finding a Wolf.
- Hit Escape, then "Save and Quit".
- Once on the World Selection Menu, where you can pick what World you want to play on; go into the settings for your World you were just on.
- If you scroll all the way to the bottom, you'll see a setting "Copy World".
- Create at least 4-5 Copies of the World you found the Wolf on, using this Method.
- Once you have your Copies, go to the Original World and attempt to befriend the Wolf. Each Bone has a 33.3% chance of working. 5-10 Bones should be enough. If you are successful, you will see the Wolf gain a Red Collar, and Hearts will appear.
- Before switching to the next, copied World, verify your Achievement Progress by hitting Escape, and going to the Achievement Menu in the bottom right corner (it looks like a Potion). You should be able to see the Achievement in the "In Progress" Section.
- After verifying it registered you befriending the Wolf, move on to one of your Copies. Repeat the process from above on all subsequent copied worlds until you complete the Achievement.