Here is the full list of all 19 Rebirth of Island achievements.
Produce 16 items
Survive in first night
Chop down 16 wood units
Build first house
Fly to orbit on the first try
Kill the first prey
Going down into orbit
Complete training
To knock stones
Extract 8 stones
Use all tools
Сomplete the quest of a settler
Have in submission 5 residents
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