Fairly simple achievement. You only need to finish the last level of an episode to get the achievement and you can cheat.
So start a new game > The Birth > The Queen.
Now press Down, X, click RS, right to open the cheat menu. Turn on God Mode, Give All and No Clip (lets you walk through walls). Also press Up on the D-Pad to give you a map overlay in case you get lost while clipping through walls.
Since you have No Clip on, just run straight forward through the transporter, then through the wall in front of you into the purple river. Run to the end of the river and through the wall. Follow the hallway until there's the blue water. Press B to dive and follow the under water passage to the end (where the atomic health is) and the wall will open revealing the Queen. Simply kill her and the achievement is yours.