Here is the full list of all 19 Rebirth of Island achievements.
Fly to orbit on the first try
Set a target for spiders using spider's arrows
Kill 10 spiders
Сomplete the quest of a settler
Have in submission 5 residents
Kill the first prey
Send first signal
Chop down 16 wood units
Produce 16 items
Extract rare stone and go on top level
Survive in first night
Build first house
Extract 8 stones
Go down to bottom level
Use all tools
Going down into orbit
To knock stones
Complete training