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