For the achievement to become active, you must explore the sector. The sector is a single dangerous area, with an asteroid field that is safely navigable. The Boron S-ship is from the quest "Enough for This Mission." You are not allowed to leave the asteroid area. There are 5 exploratory points in the sector.
At both Ka'ak stations, there is an asteroid to be discovered. If you fly carefully there, the Ka'ak should leave you alone.
Below the jump gate is a Xenon station where there are no enemies, so you can explore it as well.
In the middle, there is another asteroid that can be approached from the right side.
Above, there is initially an inactive gate that needs to be explored.
Once you have flown everything and the achievement "Plopp" doesn't pop up, check if the asteroid area forms a Q-image as shown in the screenshot.
Tipps
Save regularly while exploring, and occasionally a Ka'ak ship may appear.
If you are already advanced in the game and have researched "Hull Technology III" at the headquarters, you can protect your ship with Hull Extension III from dangerous sectors at an appropriate shipyard, at the workbench, from the ship dealer.