Creating a UV Map for Character in Unity

This should be done in the modeling program rather than in unity.

You may want to try Blender as it is a free program. You can also get programs such as Autodesk maya and 3ds max if you are a student (or pay for a license of them).

I'm familiar with blender. I simply don't know how to create that kind of UV map.

Do you mean a uv map in general or the art style used in AngryBots? If you just need help learning to uv map there are many tutorials, if you mean the art style then you will simply have to study the textures used in AngryBots and develop an artistic style from there.

I mean in general. Like how to get the legs, arms, chest and back setup in the uv map.