sed can accomplish this in a single line, albeit in a rather convoluted way.

ls | sed 's/(.*)(-.*)/mv "&" "1.mp3"/' | bash

This first lists the files in the current directory (assuming all the files you want to rename are in the current directory), and then uses sed's s/regex/replacement command to generate a sensible mv command which is then piped to bash which executes it. This assumes all of your files are something of the form "A-C.mp3" or "A - B-C.mp3". Here is how it works:

The regex part of the sed command is

(.*)(-.*)

this "groups" the name into two groupings (delimited with escaped parentheses): one matching ".*" (any number of any character) and another matching "-.*", a dash followed by any number of any character. Notice that this matches the entire filename (in two groups). Also note that since "greedy" regex is used, the first group will match "A" in "A-C.mp3" and "A - B", not just "A ", in "A - B-C.mp3", as wanted.

The replacement part of the sed command is

mv "&" "1.mp3"/

Note that an & character instructs sed to insert the entire pattern that matched regex, in this case that is the entire filename, and the 1 instructs sed to insert the part of the filename that matched the first grouping ".*". These two are combined with an preceding mv and a trailing .mp3, with escaped quotation marks to produce a sensible rename command. For example, for "A - B-C.mp3", the full sed command will produce:

mv "A - B-C.mp3" "A - B.mp3"

And finally all of this is piped to bash, which happily executes the mv (rename) command.