I can’t find any documentation that will allow adding any tag attributes to the wp_editor except for the id. You’ve got two options that I can think of. The first is to include a jQuery dependent (or not) javascript file which will add the required attribute to the editor textarea after the DOM is fully rendered.
The other option is to include a validation function either server side or browser side to make sure the data is present. I suggest this approach because the required attribute is not universally implemented across browsers.
Your code won’t work because there’s no apply_filter function that fires on $statement.