Holding shift just constrains the transform.
Basically there is no way to stop losing the pics resolution. Especially with the distort transform.

As ChuckEvans and LeFrog said start big and reduce the image last(if you can) and don't reduce smaller than you want and then enlarge again.

And try to transform as little as possible. Less is more.

Quoted from the Photoshop help files
"When transforming a bitmap image (versus a shape or path), it becomes slightly less sharp each time you commit a transformation; therefore, performing multiple commands before applying the cumulative transformation is preferable to applying each transformation separately."