What does 大秀香肩美背mean?
We all know that 大 means big. It can be used on things like 大香蕉（big banana). 大 can also be used to verb. When used to verb it means this action is really big. So 大 + verb means doing something really hard or doing something in a high profile or doing something very much(like thank you very much )

So here 熊乃瑾 was trying so hard to "秀香肩美背" in a high profile.

Similar examples: 

大展宏图， 大赦天下, 大快人心