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