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