Something lightweight like "papers please" where you are the team leader trying to bring down some large invading monster of sorts. Every movie has this team where they have to "try everything" before they just simply send in the hero and he does what the plot needs.
Can have ways of figuring out weaknesses
Not necessarily violent -- may sometimes require violence
Reports damage caused to environment by you and/or the beast, can aggregate "score" in this way
Reports damaged avoided by taking steps, can aggregate another "score" in this fashion
-- allows players to be proud of how much destruction they've caused/avoided in "bringing it down"
Player can "scan" or query certain identifiable features on the monster. There could be sub-features, so a player may do an infrared scan, determine the monster has a nervous system, and then sub-scan for brain wave origin. This allows them now to strike at the brain, conceptually, with weaponry or communication
Infrared scan
Xray scan
External 360 view
Look for orifices, heartbeat, blood flow, nervous system, behavioral identifiers (is it just trying to go home?) -- players may "bring down" nice monsters without realizing their actions