How to transfers AVCHD and other videos to Galaxy S4 easily: (provided that the output quality could be reserved well.)
Here I take macx mobile video converter as an example:
Firstly, run macx mobile video converter on Mac, added video files to this program;
Secondly, choose Galaxy S4 as output directly. You can also crop the video file, extract favorite segment, etc in "Edit" setting.
Last step, begin convert AVCHD to Galaxy S4.

This is my personal experience. Certainly, there are many other software alternative. What's your choice?