First of all you would need to back up your website just to make sure you prevent loosing any of your content. You would need to open the Theme Options in a separate tab in your browser and keep in open. Then go to appearance, select default theme and delete Axioma theme, Then install and activate updated theme theme from the updated theme bundle you’ve re-downloaded from the themeforest. Once you done with that go back to that tab with the Theme Options and click there Save all changes, by doing it this way none of the customization added through Theme Options would be lost. And also you would need to update all theme plugins, you can just deactivate these and delete, and then install plugins from updated theme bundle.