I am not afraid of anyone laughing at me for cowardice.
这句话不简单啊!不过你放心我的答案!
若要用你那句的句式也可以的：
No matter who laughs at my cowardice,I don't fear!
不过laugh at 后面一半是加“人”的,你直接加my cowardice似乎也不太对,要不这样吧：No matter who laughs at me for my cowardice,I don't fear!(我查过laugh for 加原因,连在一起用应该没问题.)
我刚问了一下我的外教,他说可以用laughs at my cowardice,所以可以这样说：No matter who laughs at my cowardice,I don't fear!