If you haven't lost those officers, take out the Chimera's two helpers (Seeder Elder, Tactical Elder), then damage the Chimera after they're gone. (It's okay to apply debuffs to the Chimera before the other Chruul are gone.) Use whatever Tier I ships you have to finish off the helpers if necessary. If/when you don't have any Tier I ships or Level 2 officers left, move to the next section.

When selecting new officers, pick whoever has an attack that inflicts Ship Disable. For example, Backstab Maneuver, Suicide Run, and Death From Above all inflict Ship Disable. If Ship Disable isn't available, pick Bend Spacetime, Cloak, or something else that you can use to get more hits in before you die. To train your new officers, have one start clearing out a room in the Starbase. If that isn't available, you'll just have to use whatever you started with (hopefully you have officers starting at level 4 by now). Before you start time, go to Ship Construction and queue three Federation Shuttles. When your officer runs into an enemy, fight! Deploy the Officers you want to level up. When you get to promote them, select the abilities you picked them for.

When your Shuttles are ready and your officers have reached Level 2, send your new fleet of Shuttles to attack the Chimera.

Use your abilities first, then Pew Pew. Be sure not to use a Ship Disable attack when the Chimera is already disabled. If you lose the fleet, go back to step two. Eventually, you should reach a point like this:


Congratulations! Enjoy the stats and achievements list.