You don't have to combine the two achievements (Expert and Pacifist), but it's doable so here's how...
For Expert you need to beat the puzzle in less than 3:00 minutes. So follow what I do and you'll find it rather easy.
For Pacifist, simply make sure you spawn a Decoy on the little rails so that the RPG turrets don't hit the Machine turrets. You CAN run to the other room and not die. Just don't stop for a second and always spawn a Decoy in front of you exactly at the spot that you will pass by the time the turrets react.
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