Here's how the federation can destroy all life in the star wars galaxy using federation technology.
This is assuming that the federation have a means to travel to the star wars galaxy.
Here are the easy steps
1) Take a federation starship to the star wars galaxy. Preferably toward the center of their galaxy but anywhere in their galaxy should be fine.
2) Make it clear to any aliens that you are on a mission of peaceful exploration that way they don't consider you a threat and attack your ship.
3) Modify the vessels main deflector to emit an inverse tachyon pulse (a form of technology used to scan for temporal disturbances and to scan beyond subspace barriers) and then emit the tachyon pulse.
4) go back to federation space and wait about 6 years
5) repeat steps 1 to 3 and fire another inverse tachyon pulse at the same coordinates
6) go back to federation space and wait about 25 years
7) repeat steps 1 to 3 and fire another inverse tachyon pulse at the same coordinates
Ok now you're done. Initiating a tachyon pulse at the same coordinates in these 3 time periods should rupture the subspace barrier and create an anomaly or more specifically an anti-time reaction. The anti-time eruption will travel backward in time and grow in size until it covers their entire galaxy which then stops all life from ever forming in their galaxy.
It's possible that the waiting times in steps 4 and 6 don't need to be as long as I made them but just to be on the safe side I used the same length of time between attempts which was done on star trek.
Enjoy defeating star wars if you ever get bored and want to do this.

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First of all you do need to transport the whole ship or are you going to steal local ship the same ship THREE different times at intervals of 6 and 25 years that is assuming that the alt verse ships are even capable of performing the required task.
Secondly I haven't forgotten the events of one of my favorite Voyager episodes. If you had READ THE POST you would of seen that like the original premise of the thread confined it to the tech and capabilities of the FEDERATION not the Voth. You can see the suprise on Janeways face at her SHIP being transpoted inside another, to her it was an imposibility a moment ago. To reiterate the point the FEDERATION has never demonstrated such a capacity.
But you don't need ships to travel to the mirror universe. The only time a vessel was used to get to the mirror universe was when they took a wrong turn in the wormhole. The other times they used transporters to do it.
Actually the premise tells you how to destroy the star wars galaxy with federation technology. It doesn't say you can't use non-federation technology to save yourself afterward.
Your premise actually says precious little about saving your own ass. Which is why you had to use the alternate universe idea when it was made bloody apparent that the idea was suicidal in nature. Unless you can rationally explain the FEDERATION using VOTH technology especially since there in the delta quadrant and the government dislikes humans, then this is just another cheap cop-out and a pathetic excuse. The entire idea of using another cultures equipment to save your ass is weak in of itself, its like the klingons are attacked by the dominion so the klingons will start to use borg tech to save themselves. You see if you replace the names and it seems ludicrous then perhaps something is very wrong with the statement.