Help needed, dear Android users

Good day to all the bright minds out there.

I'm using a Galaxy Nexus bought last year in the month of May. Currently, it is running on Android 4.3.

The main issue I'm facing is a constant lag in the phone's system performance. As a result of this, I thought of factory resetting my phone. However, I have been unable to take a backup of all my apps, media and settings.

I've never performed a factory reset before and hence I'm a little skeptical about the entire process. The absence of an external memory card in Samsung Galaxy Nexus phones further alleviates my problems.

Please suggest a way/method through which I can take a backup of my apps alongwith my other data and successully restore my phone to original state after factory resetting.

Note: In case this question has been answered in a previous forum post, please guide me to the post.

Thank you all very much.