I tried to install and create Linux box in our Hyper-V servers and I failed. Common issues is the Network Adapter cannot be installed, therefore there will be no eth0 or whatsoever. Doing some research, You just need Linux integrated services for Hyper-V. This is set of drivers that enable synthetic device support in supported Linux virtual machines under Hyper-V. So here it is:

Linux Integration Services for Hyper-V

Download and just follow the documentation Inside.