Before DRM can open DVD files, they have to have any protection removed. It's also a good idea to remove any audio or subtitle streams you don't want to keep so you'll know exactly what the size of the disc will be while you're editing it in DRM. I'm going to accomplish both things at once with DVD Shrink.
Ripping The Disc
Open DVD Shrink and click the Open Disc button on the far left side of the toolbar. Select the drive you want to rip from and click the OK button. When Shrink is finished analyzing the DVD, go to the DVD Structure pane (on the left side at the top) and select the top item (DVD_VIDEO). On the right side of the screen (in the Compression Settings tab), select the drop down list under Video and set it to No Compression.
Stripping Extra Streams From The Movie
Back under DVD Structure, select the folder that says Main Movie and look at the list of languages in the Compression Settings tab. There are 4 different audio streams, including one that's in French. Start by removing the French audio. Before removing anything else you should use the Preview pane (on the left side at the bottom) to listen to each one. After you start playing the preview, change the audio stream that's playing by right clicking on the preview, selecting Audio from the popup menu, and then selecting each English audio stream, one at a time. You'll find that the third audio stream (AC3 2-ch English) is director commentary and the fourth one is just the music, with no dialog or sound effects.
Since the idea is to keep as much of the extras as possible, remove both of those audio streams as well. Even though I don't care about the French subtitles, as a rule I keep all subtitles because they don't make a big enough difference in the final size of the DVD to matter. The French subtitle stream is only 2MB, which amounts to less than 0.5% of the disc.
Examining Extras
Stop the preview and expand the Extras folder on the DVD Structure pane by clicking the + next to the Extras folder. There are 28 different titles listed, numbered 2-29. Select each one, look at the audio and subtitle streams on the Compression Settings pane, and preview it to see what it is.
Since the main movie (after removing audio streams) and all the menus are only 3,438MB together, there will be room to keep some of the extras and still make a backup with no compression. A couple of the extras (titles 13 and 14) are big enough that they won't fit with the menus, so you already know you can't keep all of them, but multiple extras can potentially be kept.
While you're previewing each title, make sure to look at the Compression Settings tab to find out if there are any streams that you might want to remove. Titles 3-10 each have two audio streams.
By listening to the second audio stream on each (like you did with the main movie) you'll find that these titles are deleted scenes, and the second audio stream is director's commentary for them. Unlike the main movie, however, you won't save a significant amount of space by removing these streams. They only add up to about 9MB between them, and once again that's an insignificant percentage of the size of a blank DVD and there's really nothing to gain by removing them, so you can leave them in.
Watch The Beginning Of The Movie
If you're not already familiar with what the first items to play on the DVD are, make sure you watch it, either on a standalone DVD player or a software player like PowerDVD or WinDVD. You need to find out if anything plays before the main menu so you can get rid of them. Once Upon A Time In Mexico has the standard copyright warning and studio screens that play first, as well as a screen that shows you the movie's MPAA rating, but after that there are also two movie previews.
Open DVD Shrink and click the Open Disc button on the far left side of the toolbar. Select the drive you want to rip from and click the OK button. When Shrink is finished analyzing the DVD, go to the DVD Structure pane (on the left side at the top) and select the top item (DVD_VIDEO). On the right side of the screen (in the Compression Settings tab), select the drop down list under Video and set it to No Compression. 
Stop the preview and expand the Extras folder on the DVD Structure pane by clicking the + next to the Extras folder. There are 28 different titles listed, numbered 2-29. Select each one, look at the audio and subtitle streams on the Compression Settings pane, and preview it to see what it is.
