GitHub only exposes the way to show diff between two commits.
Provided those tags actually point to commits, the Url format would be something like
https://github.com/{user}/{repository}/compare/{from-tag}...{until-tag}
As an example, https://github.com/libgit2/libgit2sharp/compare/v0.9.0…v0.9.5 shows the diff between two versions of the LibGit2Sharp project. This diff includes all the modified files.
If you want to retrieve a URL that targets a specific file:
- Switch to the Files Changed tab

- Click on the Show Diff Stats button (This will display the list of modified files as links)

- Copy to the clipboard the link of the specific file you’re after… and Tada! You’re done.
For instance, given the diff above, the link https://github.com/libgit2/libgit2sharp/compare/v0.9.0…v0.9.5#diff-11 will point to the LazyFixtures.cs changes that occured between version v0.9.0 and v0.9.5.
Update
Following your comment which states that your diff is too big to be rendered through the Web interface, how about reverting to good old command line tooling? You could redirect the output of the diff to a file and then send the file as an email attachment.
$ git diff v0.9.0 v0.9.5 -- LibGit2Sharp.Tests/LazyFixture.cs > /tmp/lazyfixture.diff