This will take you quite some time, as you can't just travel to another system. First you must earn enough money to spawn trapped boss and then pay to unlock the next warp. Below are the systems and planets that you will need to buy a building for.
So just head to each of the planets listed below, and build at least one building on each to unlock this achievement.
Sol:
Mercury
Venus
Earth
Mars
Jupiter
Saturn
Uranus
Neptune
Galene:
Bloobus Majors
Bloobus Minoris
Squibblius
Quelbrog
Quinton
Nigel
Saquanus
Casin:
Yuri L
Raeez M
Maduna's Retreat
Bingham Alpha
Vent:
Dragon B3
Auron Ridi II
Meni Prime
Gorgon X
Artemis T2
Hoonoo 69
Puri
Voltimus:
Quatica
Coralion
Bub Bub
Rivaria
Funtain
Glub Glub
Taria Trench
Queytar
Horus:
Sekhmet
Seth
Thoth
Anubis
Osiris
But
I apologise for not including amounts for unlocking each new system, but if you head over to the Warp you will be able to see just how much is required.