There is no such thing as the 'Windows 8 Browser'. You can use any browser and I can think of no reason whatsoever why anyone would want to use the dire Internet Explorer that comes with it. (Firefox is a zillion times better, as is Chrome).
However I assume that you're using Internet Explorer 11 which is actually two separate programs in Windows 8 (but, fortunately here, they share the same history files).
You can't access the detail of Internet Explorer's history from the app version. You need to launch the desktop version. Press Alt+C to open the 'Favorites and History' menu. Click on the 'History' tab. From there, you should be able to delete individual items via right-clicking on them.
However one of the (many) faults of Windows 8.1 is that it doesn't allow you to open the desktop version of IE11 (unless there's now a patch that I don't know about). So if you've got Windows 8.1, rather than just Windows 8, you might still have problems.
Get a decent browser!