I am using JMeter for testing the server side performance of our Mobile App.
What tool can I use to test the client side performance of the app?
I know there is a plug in for JMeter but as far as I am concerned what can be used for Mobile Apps?
From your description of the question it would seem that you want to do Load/Stress/Volume testing of the mobile application.
For that you use Jmeter or apptim (I haven't used this personally so won't comment on it) as suggested by Kalei, or any other tool that others might suggest.
But, when talking about performance testing why would you limit yourself to only hitting multiple requests (Load/Stress/Volume etc testing)? This would only test the load your server can handle or the interaction between your application and the server. It won't test how the application itself performs on the device.
There's a lot more to mobile application's performance testing. Here are a few things you can test as part of performance testing,
Check out Apptim. It was designed specifically for client side performance of native apps and can work for hybrid as well.
This is a good article that explains how to run a test with Apptim and can give you an idea if it is the right fit: https://blog.apptim.com/mobile-performance-testing/
Disclaimer, I work there as a product marketer, but I really do feel that this solution will be useful to you.