Here is the full list of all 16 Unclaimed World achievements.
You escaped Tutorial Island!
You reached the objective in 'The Clay Pit'!
You reached the objective in 'Making Headway'!
Complete 'Twinkler Island' (Normal or Hard) with no deaths and no-one leaving
Kill 300 swarmers in 'Muckroot Mining Site'
Complete 'Twinkler Island' (Normal or Hard) without killing any twinklers, thunder chickens, bajingans, bush dragons or binal rats.
Produce 10 blackpowder rifles and 20 blackpowder rifle ammo in 'Fields of Tau Ceti' (Normal or Hard)
In 'Fields of Tau Ceti' (Normal or Hard), get 12 population and ratings of 35% in Food, Security and Comfort without establishing any farm plots, fish traps or greenhouses
In 'Fields of Tau Ceti' (Normal or Hard), produce 50 thunder chicken tanned hides, 40 whipjaw tanned hides and 20 megapod tanned hides
In 'Muckroot Mining Site', get 15 population and ratings of 45% in Food, Security and Comfort without refining any scandium or terbium
In 'Fields of Tau Ceti' (Normal or Hard), have 3 colonists with the same surname
Kill a twinkler with the spray gun sentry in 'Twinkler Island'
In 'Muckroot Mining Site', get 20 population, 1000 credits and ratings of 45% in Food, Security and Comfort
In 'Fields of Tau Ceti' (Hard): Survive for 2 years with at least 5 members without advancing the tech tiers.
In 'The Clay Pit', get 15 population, 200 credits and 40% in Food, Security and Comfort
Complete 'Making Headway' without producing any rubber parts.