Whilst I plan to tackle a proper Apple ][ Hi-Res mode in a future version of Retrospecs, you can create a reasonable facsimile of the aesthetic using the newly released Retrospecs v2.9 - here's how!
First off, you'll need an unlocked version of Retrospecs, as you're going to create a custom emulation.
Secondly, you're going to need to save the Apple ][ Hi-Res palette image below onto your device - I'd recommend saving it in Files, but your Photo Library should be fine as well. (To save the image, just hold down on it and a dialog should appear.)
The first step is to create a new custom emulation and to do that we need to be in the Converter, so on the app home screen select an image or take a photo to get started. Once you've done this you'll be transferred into the Converter.
There are two ways to create a custom emulation in the Converter - you can either…
…or you can use the super secret shortcut and simply hold two fingers on the preview image. (I should probably have mentioned that first.)
Now it's time to customise the emulation engine we're going to use.
The next step is to create a new custom palette using the image we saved at the start and to do that we need to use the custom palette editor.
Finally, we need to set the screen size, so select the Screen tab and entering the following values…
By now, things should be hopefully be looking familiar if you're ever used an Apple ][ before.
Now that we've created our custom emulation we need to save it, so simply select the add (+) icon and enter a name. ("Apple ][ Hi-Res" if you want to be all arty about it.) You can now return to the converter using the < Converter back navigation option. As you can see, your new emulation now shows up in the Mode list when the Custom system is selected.
To get the best results from your shiny new custom emulation, I'd recommend…
However, as with everything in Retrospecs, you'll get the best results by experimenting.