The easiest way to snag this trophy is simply beating the game. Once you do that, you will unlock a few other frames for Jehuty, including Naked Jehuty.
The benefits of Naked Jehuty are the following:
- Hits harder on all standard attacks
- Hits harder on all subweapon attacks
- Unlimited subweapon energy
That last one is the most beneficial, as you can go into an enemy filled area and seriously spam the crap out of any subweapon.
After you complete the game, start a new game on easy. Select Naked Jehuty, and play with all subweapons unlocked. Doing a pure speed run will get you to this rescue mission in ~20 minutes.
Save at the start of this mission. I can not stress that enough. If you fail to get the SS rank, all you need to do is reload the save and try again.
Then you just need to kill spiders. The best subweapon for the job: Comet. The Comet subweapon will eliminate just the enemies and cause damn near no damage to surrounding areas and/or friendly LEV's. Spam the Comet and you should be fine.
Just like the first game, this rescue mission requires all buildings, survivors and LEV's unharmed for the top rating (SS).
Questions, corrections and neg vote justifications in the comments below.