best way to start is map your app… what does it talk to, what are the dependencies…. a good old mind map or diagram..
Take everything into account and try to test each step/connection/dependency. Not sure if you can solve it without any 3rd party tooling but you will get a very good insight in your app.
eG uses Itexis for in app mouse click which is interesting (Itexis is a 3rd party tool for them) as it show where the slowness is… it does not show why it is there. for that you need to monitor the backend/resource… perhaps you know which part of the app is slow and when you map it on a whiteboard you can logically work to that component…
Best of luck… fun job (always my favorite part of being a consukltant) but not a simple one