Make it to the Sun level (follow the walkthrough if you are stuck), and achieve the following first quest endings:
*** Spoiler - click to reveal ***
For all the endings, there are consoles down at the base of the alien craft that you need to interact with. Fly down to the bottom (either by entering the tube and flying down) or fly down outside the craft. Remember that Z is used to fly downward (may not have been needed until now as this is the first 0 G level). Achieve all the following endings:
- Fail and cause the A'kraam to destroy the solar system: Find the communications console, walk into it, and choose the option to declare war with the A'kraam. The A'kraam will quickly activate their device and destroy the entire solar system! You will then be sent back in time and given another chance.
- Negotiate with the A'kraam: Find the communications console, walk into it, and choose the option for peace. After some conversation, congratulations, Earth is saved!
- Call out the A'kraam: Find the communications console, walk into it, and tell them that they have committed an act of war (but don't declare war on them). They will retaliate and activate the craft to fire on the Earth. This will initiate a waypoint mission to quickly deploy nanites in targeted areas to cause the energy pulse to destroy their ship rather than initiate a solar flare. See the "Blur 42" mission for the likely most optimal way to beat this mission. You don't have to fail this mission to trigger this achievement, just beat this one. Congratulations, you saved Earth (again).
- Fly the A'kraam ship into the sun: Find the Navigation console, walk into it, enter through the dialogue, and press E to activate the console. Hurry back to the portal and make a hasty escape before the ship is destroyed. Congratulations Earth is saved, and you should now have the "Many Worlds Interpretation" achievement.
For some fun: Google the "Many Worlds Interpretation" to learn an interesting idea on how Quantum Mechanics might work fundamentally. This is what this achievement is in reference to. I personally don't believe it is the correct interpretation, but it is at least very interesting to think about. I believe there are many interesting new technologies we can develop in real life using Quantum Mechanics (Quantum Computers for example).