Despite the fact I only use Visual Studio to edit Xamarin.iOS project files I experienced the situation when Visual Studio unexpectedly thought I used Xcode. Moreover, Visual Studio broke my project because it did not allow me to use an iOS Designer. Ironically the storyboard file was created in earlier version of Visual Studio. My first attempt to workaround this bug was successful and here is how I you can do it too.

First, open another storyboard file and check whether iOS Designer failing to load all storyboard files or just a specific one. When one of your storyboard files opens successfully note the its tools version. Then downgrade the storyboard which you cannot open to this version.
- Right click on storyboard file.
- Choose Open with…
- Select XML (Text) Editor with Encoding and click to OK.
- Keep (Auto-Detect) option and click to OK.
- In the document element copy/paste the value of toolsVersion attribute.
Of course, every workaround may have side effects that will occur in the future. I highly recommend using version control to have the ability to revert all changes.