When playing as a Sniper you'll generally be doing backup support for the rest of your team. Before attempting Inconceivable, build up the levels of the following cards:
For the first 9 waves you won't be doing much, just hanging back and picking off the occasional Swarm or bot with a headshot. On wave 10, stick by the Fabricator and use your Radar Ping to mark targets for your team. Using this in conjunction with Called Shot results in more damage being done, so use 2-3 pings spaced out enough to mark every enemy. If you don't have a Hammer of Dawn soldier, use Sniper Strikes to clear the enemies and damage the boss as well. On wave 11, go back to picking off occasional enemies. Once you hit wave 17 stand by the Fabricator and ping every wave, using strikes on wave 20. After you get to wave 37, start pinging and striking every wave since you should have enough power to allow it. Also be sure to use your Team Revive if people go down on these later waves, since they'll generally have mission-vital weapons like shock grenades and dropshots that would be lost upon death. Keep pinging and striking your way to victory!