This achievement is basically free, since you need to defeat Mama Bear in order to progress.
She has 4 attacks: three jabs, spinning, marching to you, morphing into a spikeball.
To dodge the three jabs, you just need to keep on running.
To avoid the spinning attack, use Speed Boost and just run.
When she's marching towards you, you need to use Primal Fear when a trigger teddy is nearby Mama Bear to make it explode and damage her.
Lastly, when she becomes a spikeball, use Speed Boost and run away until she finishes her attack.
Currently, this achievement is unobtainable.