Here is the full list of all 17 Kasi achievements.
The base game contains 13 achievements, and there is 1 DLC pack containing 4 achievements.
Have 20 fruits at one time
Have 20 flowers at one time
Grow as high as the sun at its apex
Have 50 moon leaves
Exceed 300% light during a blood moon
Burst 200 stars with one plant
Have 50 branches
Have 10 birds on your branches at once
Root a vine back into the ground
Grow a fruit
Reach 80% maximum light with 20 or more leaves
Shoo a bird
Grow a flower and start pollination
Feed the spider until it is fully grown
Keep time stopped for 5 days
Have a plant split into two plants
Grow for one year