Back away from the first fight at the Starbase. The Starbase will destroy two Venturi ships, and you have to destroy one. Warp to Omega 12-300. Scan the derelict ship and hail them. You will notice that the ship's status is blue, which means that it will not attack you. Scan all the ships to turn them blue, except for the ship with Alshoff. Target his phasers and destroy them. Now target his engineering section and destroy him. This is much easier than fighting at least six ships during this mission.
Boosting your starship: When boosting your shields, phasers, and photon torpedoes you cannot go to warp. To remedy this, go to Green Alert. You may now warp because those systems are no longer activated.