The Mothership can only be destroyed on the last mission.
You'll need a non-homing rocket launcher for this and a primary weapon of your choosing for the other foes (I recommend a decent machine gun).
Kill a bunch of the enemy units and eventually the Mothership will expose a giant laser weapon. Destroy this QUICKLY with your rocket launcher.
Next it will expose it's core occasionally while constantly firing at you from spinning plates. These plates can be destroyed easily, but your main target is the core whenever it is exposed.
Note 1: DON'T use homing missiles as they won't target the Mothership and you won't be able to hit it.
Note 2: If the plates keep hitting you with their attacks you can either keep moving or shoot a lot of them down.