Hi,
ProTecKs solution sums this achievement up excellently.
Just some additional info:
The achievement is unmissable (for killing the first boss) and is part of the normal progression in this game.The boss is located in the stage Dark Forest VIII (which is the first world)
I had the feeling that you had to time the usage of the teleporter very well. For me it always seemed to work when my ME fell on the open "brain" when the opening was at it's biggest.
If someone has troubles with the boss fight please refer to the video below .
(video credit: Gilgy tigrex)
Hope this helps you guys.
Any improvements? Please let me know in the comments below!