Defeating Shinnok
Defeating Shinnok is rather quick, if done correctly. Whenever he tries to attack you, use an Ice Blast to freeze him. Then go through the correct Portal (at either side of the room, obviously depending on Shinnok's position) to come up behing Shinnok. Now instead of attacking him, use the Take button to steal his Amulet.
You should hear him scream: "NO, The Amulet". Now you just have to defeat his beast form. You can then run into the Portal available to escape.
Defeating Shinnok's Beast Form
To defeat Shinnok in this form, you should either try to position yourself in a way whereby you can just run to the portal and attack. You can also try keeping your distance from him and attacking him with Polar Blasts.
Both ways are reasonably safe!
