There is no optimal champion for achieving this since it's heavily teamplay based, however you can look for a champion that fulfills one or more of the following criteria:
Securing the Ascension buff through stealing is a good option, however it can be pretty hard to pull off so it's not the most secure way. Champions like Lee Sin, Elise and Cho Gath can steal rather well since they have either High mobility, High damage or both.
This is the safest way. Control the enemy team and deny the Ascension through crowd control. The only thing you have to keep in mind here that you heavily rely on your teammates to help you since your damage output won't be too high (so no stealing). Champions with Knockbacks are really strong. Good Champions Include: Lee Sin, Xin Zhao, Nautilus, Kennen, Galio. Basically everything that can keep a team busy.
You still have to win the game, and for this you will also have to be present around the shrines you have to capture. You could take the role of an assassin to deny shrines to your enemy while your team fights xerath in the middle of the map. Good champions: Talon, Akali, Zed.
Basically it's up to you what you play. It's almost impossible to gain the Icon by yourself ssince it's as I've already mentioned extremely teamplay based. If you have a good team you will get it automatically.