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 50 branches
Grow a flower and start pollination
Root a vine back into the ground
Shoo a bird
Grow a fruit
Exceed 300% light during a blood moon
Have 20 flowers at one time
Have 20 fruits at one time
Grow as high as the sun at its apex
Have 10 birds on your branches at once
Burst 200 stars with one plant
Have 50 moon leaves
Reach 80% maximum light with 20 or more leaves
Feed the spider until it is fully grown
Have a plant split into two plants
Grow for one year
Keep time stopped for 5 days