You need to Scan all Animals on 10 Planets. Easy you say? Not so much.
There are two ways to go about this.
The Hard Way
Just thoroughly search every planet you visit and keep your eye on the Discoveries tab. The animals which have not been scanned will appear as entries declaring rarity (this is very relative, as I've been looking fruitlessly on some planets for supposedly "Common" species for hours to no avail. At the very least it should tell you if the beasties appear around buildings, in caverns or underwater.
But like I said, this is VERY random. There are planets with some 12-14 different species and those can be a real PAIN. A couple of times I found that I was seeing red blips underground and I assumed that there were in a cave. To my surprise when I dug with the Manipulator I found that they were just moving through solid soil for no apparent reason.
So unless you intend to spend hours on this achievement there is the...
The Right Way
Your best bet is to find Anomalous planets, you will know when you land on them since nor the fauna look like animals nor the flora like plants. These places are like something out of a mild acid trip. On these planets, there is usually just one type of creature and they are not really hard to find. These occur more often around the rarer types of stars, but you can even find some around Yellow ones.
As of writing this, I am halfway there myself and I've just about had enough of looking in regular planets. I have several planets with 1 or 2 species left to find and I just quit them after hours of having no luck with the last one or two species.
Good luck and remember to check the skies and bodies of water when looking in normal planets!