Even today it takes quite a few attempts to get an SS rank - and thus The Good Rescuer PSN trophy - for the first mission in The 2nd Runner.
First several attempts - learn the spawn points, number that spawns.
Next attempts: Try your best to reach all these spawn points quick as you can use the best methods and angles to take them all out. Make sure the spiders towards the end don't go too far or the allies will fire and clumsily damage some of the buildings. Even a 99% on building integrity is not enough for the SS rank.
First playthrough, I recommend Phalanx (though Jehuty mentions Geyser instead). On later playthroughs, if you're not able to get this achievement on your first playthrough, you can use Homing Missiles for some easy clean up. Careful not to fire too many at a time and waste energy. One is more than enough for a spider.

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