NoSuchMethodError basically means that a class definition has changed between compile time and runtime. This can be caused by using a different version of a jar when running your application than the version things were compiled with.
It looks like sometime between Jetty 8 and 9 the getConnection method was removed from Request
. I would check your target folder to make sure you don't have multiple versions of any jars and that the versions you are using are compatible with each other. Also make sure that however you are running Jetty, it's the same version as the libraries your application depends on.
You might also run maven dependency:tree
to check that versions in your pom aren't being overridden in unexpected ways.