Simply put, no, not easily.
You can certainly increase or decrease the audio level, the tonal quality (to a point) and even use the compressor.
The problem you are going to have is that both the vocals and the instruments are on the same audio track.
You may want to try a DAW (Digital Audio Workstation) like Protools or even Audacity where you may have better luck, depending on the plug-ins you have and patience.
Once you have “tweaked” the audio there, you can bring it back into Shotcut and replace the original audio.
Keep in mind though that even on dedicated audio software, it will be difficult as already mentioned, due to the fact that everything is on one audio track.