What you'll want to do is add the following into your responsive stylesheet...
.responsive .slideshow_container {
display: flex;
margin-bottom: -100%;
}
Then head into the slideshow's settings and hit 'yes' on "Shrink slideshow's height when width shrinks" (The default is 'no').
Tinker with the aspect ratio above the 'image behavior' field. I've got a squareish slideshow running on one of my sites, so 5:4 works best in this particular case.