In the newest version of Minecraft's Tutorial it's pretty easy to do this achievement in 5 minutes or less if you're lucky. Instead of loading a previously saved file or creating a new world select
Play Tutorial.
When the Tutorial level has loaded, press
to skip the tutorial and head forward & left through the gate. Go forward to the fountain. When you get to the fountain take another left and walk forward, you'll be at a chest with various things to tame and breed animals in it.
Take out the
10 Bones and
2 Wolf Spawners, go into the fenced off section next to the chest containing wolves. Select the Wolf Spawners by using
or
to cycle through your inventory slots until the Wolf Spawners are highlighted. To use them press
. Once there are 4 Wolves in the pen, select the Bones and "Tame" them with
. It takes at least 1 Bone to tame a Wolf, it can take over 7 to tame one as well (I just tested it a few minutes ago).
If you're lucky you'll be able to tame all 4 wolves with less than 10 Bones. If not, you can Exit without saving and repeat the process until you get the achievement!