1) Memorize the order of the colors: green - red - black - yellow - blue - purple - green (again, the sequence starts over);
2) Choose the color you want to transform the slimes into. One tip is to choose the color that already has the most slimes;
3) If you choose, for example, the color purple, focus first on changing the color of the slimes that need to go through more transformations to reach that color, that is, start focusing on the green slimes, then the red slimes and so on, following the sequence that I mentioned above;
4) Try to leave 2 or 3 slimes to make the last transformation.
With a little practice and luck, you will eventually get the achievement.