If Putin is behind the murder of Boris Nemtsov, it may be because he does not want a repeat of the Ukrainian Maidan Square protests in Russia. Putin appears to have been blindsided by the speed with which the Maidan protests ousted Ukrainian Premier Yanukovych, leading to the low grade war going on now. Putin does not want to see something similar happen to him in Russia. By killing Nemtsov, he made sure that the Russian protests would not get out of hand.
I don’t know whether Putin order Nemtsov’s murder, but I doubt that he was disappointed by it. It is unlikely that it would have happened if Putin has been strongly opposed to it, or even highly concerned about Nemtsov’s safety. Putin could have provided security for him that would have made his assassination impossible.
The fact that Putin is so closely linked to the murder raises serious human rights issues for Russia, and security concerns for many Russians unhappy with Putin. It will make it more difficult for the US to do business with him, in particular getting Russian cooperation on Iran nuclear matters. There is an outside chance that Putin might be more cooperative on Iran to ease some of the pressure resulting from the Nemtsov murder.