Trying again. (note, doing so because I really, really hate the negatives of both the OP's weapon choices AND because I'm trying to get rules down. His choices may be better anyway.) If I've made an error below, you're invited to point it out. Again, adding a rules cite (book, page, and heading) would be useful if you do.
Full auto (again), WIDE full burst, and don't forget the tracer ammo.
Assuming 24 dice for attrib+skill+ mods (including 5 for smartlink and tracer) that's ~8 hits. An F12 spirit gets 12-9=3 dice for 1 defense, leaving me 7 hits. Add 6 for the ammo is 13 net hits. That beats the sprite's 12 (hardened). For damage, then, the sprite rolls 24-1 (most auto weapons are -1 AP) for ~8 defense against penetration. The autofire does 4 hits. At that rate it'll take four shots to kill the sprite.
If this is true, a good mod is high velocity. The -11 instead of -9 to the sprite's defense dice will (usually) increase hits and final damage by 1. That's enough to drop the F12 sprite in 3 instead of 4 actions.