What is the best tool to increase sound of MTS video without need to re-encoding this video?
The setup that i use for something similar is:

Step 1 - demux

avconv -i in.mts -an -c:a copy video.mkv -c:a copy audio.ac3


Step 2 - audio editing

For this i just open my audio.ac3 in Audacity and normalise the sound. At this time it may be a good idea to try to remove the noise. I reencode into Vorbis, but it is up to you what you wish to do. Let's say you save into audio.oga

Step 3 - mux

avconv -i video.mkv -i audio.oga -c:v copy -c:a copy out.mkv


Notes


Video was getting copied all the time. So no quality loss is possible from that.
You can drop the video demuxing, and just grab it directly from the original in the third step. But i find it just makes the process much cleaner when you know where everything is.