I had a lot of trouble with this one, so I understand. Here’s what worked for me:
Don’t play any equipment or ongoing cards round 1. Miss Information’s just going to destroy them. Once she has two clues (round 2), she’s going to flip next round so you can get that stuff.
Focus entirely on maximum damage until the first two threats (the cat and the envoy) are gone. Which means that round 2 your best bet with Wraith is Improptu Invention to get Targeting Computer + throwing knives into play. That’s 8 damage a round right there to the threats. If you’re dealing single-target damage, shoot the Envoy, since the multi-target attacks are going to get rid of the cat.
If you have to discard your hand to get rid of Explosion in the Lab, discard Wraith’s. Benchmark and Idealist need the cards more.
Idealist’s priority is Giant Floaty Head to get rid of clues. Sure, Miss Information will destroy them for you, but she also triggers self-inflicted damage on all heroes when she does, and you want as little of that as possible. Nasty stuff like Orbital Bombardment is another Floaty Head target.
Beyond that, you want Armored Chassis, Intervening Path Calculator, and Smoke Bombs. This is 1 to 2 DR, depending. It’s 2 DR reliably if Benchmark’s HP is the same as Wraith and Idealist (best case) or lower. Attack targets Idealist, Smoke Bombs redirects and reduces it by 1, Benchmark is either the new target (if all HP are the same) or steps in front of Wraith with the Path Calculator if he’s not, and the chassis takes off another 1 damage.
Stun Bolt can also add 1 DR if Wraith has one in hand.
2 DR completely nullifies the Envoy and the Old Lady, and reduces the Cat’s damage to 1. Miss Information doesn’t do damage otherwise if you destroy her clues as fast as she plays them.
That leaves the environment. Specificially, Thorathian Military, Gene Bound Ravagers, and Orbital Bombardment. If Benchmark has Countermeasures in play - which I found easy to get with cards that let you dig through your trash for software - he’ll kill off wounded Torathian Military or Gene Ravagers before they can hurt anyone else. Doing 2 points to them usually isn’t too hard. If nothing else Idealist can get rid of them with Giant Floaty Head, but only if there isn’t something more important (a Clue or Orbital Bombardment).