Original, slower method
Preparation: You need a sawn-off with a lot of ammo (probably 1,000+), some reasonable method of suicide like satchels or an RPG, and some space in the Verdant Meadows Hangar or Garage. Infinite sprint from doing the Burglary missions is real handy too.
Now, go through the Black Project mission until you get the jetpack. Instead of flying over to the meeting place with the Truth, fly South to the quarry. Then land near the crane and walk into the red marker; you can press Y/triangle/enter to enter the crane and then when you exit back out the jetpack is gone. The good news is that you can now use whatever weapon you want. The bad news is that the jetpack is only sorta gone and you can't actually enter any other vehicles. Note that the other enterable cranes (Doherty construction site, LV casino one, probably I/E crane too if it's open) should work too, but the quarry seemed to be closest.
Next, you have to run back to the meeting place. It's a good idea to hit the Cluckin' Bell or a vending machine on the way there to reset the hunger counter. Once you get to the meeting place, stay away from the red marker and whip out the sawn-off. Blast the Mothership backwards and off the cliff; the goal is for it to land near the paved road. Depending on how the Mothership lands, it may or may not explode. The time I successfully did this, it had exploded from landing on its roof. I have not yet tested to see if this is necessary or not.
Follow it down by either running back along the dirt path or grabbing the parachute and doing a short base jump. Now simply blast it back to Verdant Meadows along the road. No traffic will spawn and your wanted level is probably frozen so you don't have to worry about any cars or cops getting in the way. Once you get back to Verdant Meadows, blast it into the hangar or garage. Then, go into the garage with it and kill yourself. When I did it, I dropped a few satchels on a Hydra I had parked in there, stood next to the Hydra, and blew us both up.
This will obviously fail the mission and you'll show up at the hospital next to the LV airport. Jack a ride back to Verdant Meadows and check out your new ride. From testing it looks to be bullet, damage, fire, and explosion proof and the proofings did stay through a save and reload. If you can come up with a better way to fail the mission than dying, that'd be great, but this worked for me and it didn't even require a cheat.
One other note, I tried once where it was not destroyed and after I blasted it to the hangar, I ran back to the meeting place and entered the red marker. The mission actually passes even though I didn't have the jetpack and the cutscene is pretty well empty, but the Mothership disappeared from the hangar.
Faster methods using vehicles
digimetal and serge have contributed ways to speed this up so that you can get into vehicles and push the Mothership back to the garage with that instead of having to stay on foot and use the shotguns.
serge's method is to use the Import/Export crane at the SF docks to get rid of the jetpack. Apparently, unlike with the other cranes, using this one does not strip you of the ability to use vehicles afterwards.
digimetal's method is to use a slot machine at a casino to restore this ability. My new suggested method would be to fly to LV and use the crane behind the Clown's Pocket to get rid of the jetpack, then run the short distance to Caligula's, play once at any slot machine (not video poker or anything else, it must be the slot machine). Then you can leave the casino, grab a car off the strip and go get another vehicle to push the Mothership.
Since your wanted level is suspended during this mission, the best option is probably to head to Area 69 and grab a parked Rhino and use that. Other heavy vehicles like the Dumper would probably work fine too. This speeds things up considerably, although you are still forced to kill yourself inside the garage to fail the mission and must remember to load the Mothership in the garage horizontally if it hasn't been destroyed in transport.
Edited by pdescobar, 05 April 2006 - 08:35 PM.