After struggling to get these achievements myself and turning to the forums for help i finally got them and thought I'd share the info.

Start the game on a small map with 6 oponents and hard or impossible difficulty.

Have all win conditions enabled.

Grab 2-3 planets and focus on energy, science and metals. Energy for making at least 4 strong ships, metal for filling your homeworld with defense drones, and science to make your fleet even better, and to get tech to potentially trade with enemies when they take planets on the way to your homeworld.

Once you have your setup keep your fleet on your homeworld, press Shore Leave, spend your rescoures upgrading, and wait for attack.

In order to get "The Trouble With Science" achievement; when the enemy fleet attacks your planets on the way to your homeworld, or your homeworld itself, you need to click the "negotiate" button and see if they will trade tech for a peace agreement. Sometimes they will demand a resource and sometimes tech. Save your game often and on multiple slots so you can do both achievements in one game and reload if things dont go well due to randomness.

If the AI is not attacking try taking over the homeworld of one of the weaker players to make yourself a more enticing target.

Try to make sure you don't go over 51% population and no other player does or it will result in someone getting the population victory.

Save often and in multiple slots so you have options.



Using this method myself and others have managed to get the two achievements. Good luck as the AI can be weird sometimes.

Thanks to the users of the Starships forums for all the help as that is where all the information here was gleaned.