Here is the full list of all 15 Slimes are the Strongest achievements.
Collect 42 stars
Collect 35 stars
Collect 28 stars
Collect 21 stars
Collect 14 stars
Collect 7 stars
Collect 49 stars
Collect 56 stars
Collect 63 stars
Collect 70 stars
Collect 77 stars
Collect 84 stars
Collect 91 stars
Collect 98 stars
Collect 105 stars