In case you are facing this issue where your @Ajax.BeginForm or any other @Ajax helper method doesn't work as expected. ie it opens new window instead of sending partial request and updating the same page. Here is the solution.
1. Go to Manage NuGet Packages .... by right clicking on the Project from the Solution Explorer.
2. Try to find out "Microsoft jQuery Unobtrusive Ajax" by using Search box online.
3. Install it.
4. Installing "Microsoft jQuery Unobtrusive Ajax", adds "~/Scripts/jquery.unobtrusive-ajax.min.js" file.
Now, try any of the @Ajax helper method and it works like a charm !