Here is the full list of all 15 Slimes are the Strongest achievements.
Collect 7 stars
Collect 14 stars
Collect 21 stars
Collect 28 stars
Collect 35 stars
Collect 42 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