Stabilize a 12V DC supply (from Lipo)
Without a circuit, the suggestion can only be to use a choke to reduce the very sharp and almost invisible thin spikes and then use a linear regulator to stabilise the rest. Keep in mind that you don't need perfectly smooth output, the amplifier is partially insensitive to them, it works (simplifying a lot) as regulator too.

Check also http://www.linear.com/docs/11877 (Minimizing Switching Regulator Residue
in Linear Regulator Outputs) that explains everything. You don't need to achieve the same results, since an audio amplifier is not that sensitive to input voltage, just get the idea behind the article.