You don't even have the remove the movement. Just remove the bezel by removing the 8 nut and carefully lifting up, then separate the rubber seal and the tachy ring from the bezel. Press on the outside of the crystal with your thumbs or a crystal press to remove it, noting which way the bevel on the crystal is, then CAREFULLY use a crystal press with the appropriate dies to pop in the new crystal. You may have a plastic ring on the inside of the bezel, it must be there for the new crystal to be seated properly.
Alternatively, you could just bring in the bezel and crystal to a watchmaker, and they probably will do it for way less than the insane price of $150. I got mine done for ~$8, which was a pretty good deal considering a crystal press from Harbor Freight is something like $14.