You could install a web proxy on your router or a computer and there are even web proxies on iOS like Charles Proxy.
There are great tutorials on the site above using the Mac / Linux / Windows version of this to debug and investigate ios / iPhone traffic. The iOS app to run this on the device itself is here: Charles Proxy by XK72
You should try this tool https://www.ssllabs.com/ssltest to grab detail information about Protocols, cipher suites, Handshake Simulation. It will help to know the configuration of any SSL web server.