Here is the full list of all 106 Unnamed Space Idle achievements.
Reach Sector 56
Complete 1000 Warps
Gain 100 Total Crew Levels
Gain 1e35 Research
Destroy 8e6 Enemies
Reach Sector 46 with the basic ship starting from Sector 1
Reach Sector 30 with the basic ship starting from Sector 1
Reach Sector 18 with the basic ship starting from Sector 1
Reach Sector 5 with the basic ship starting from Sector 1
Sustain 448 Power Boost levels for 5+ minutes
Reach 1e17 Compute Levels
Clear 58 unique sectors
Make all synth T5 recipes infinite
Complete 10 Challenges
Reach Sector 42
Gain 1e23 Research
Make all synth T4 recipes infinite
Sustain 112 Power Boost levels for 5+ minutes
Destroy 2e6 Enemies
Reach 1e13 Compute Levels
Gain 1e19 Research
Sustain 28 Power Boost levels for 5+ minutes
Complete 144 Warps
Gain 1e15 Research
Make all synth T3 recipes infinite
Sustain 7 Power Boosts for 5+ minutes
Reach 1e9 Compute Levels
Reach Sector 30
Clear 32 unique sectors
Gain 1e11 Research
Complete 36 Warps
Complete 4 Challenges
Make all synth T2 recipes infinite
Complete 4 Warps
Max Out 16 Unique Void Shards
Sustain 3 Power Boosts for 5+ minutes
Gain 1e7 Research
Destroy 5e5 Enemies
Complete 1 Challenge
Reach Sector 18
Emergency Retreat 1000 Times
Make all synth T1 recipes infinite
Emergency Retreat 100 Times
Clear 12 unique sectors
Reach 1e5 Compute Levels
Gain 1000 Research
Sustain 1 Power Boost for 5+ minutes
Max Out 2 Unique Void Shards
Destroy 10,000 Enemies
Reach Sector 5
Reach 1000 Compute Levels
Emergency Retreat 10 Times
Destroy 100 Enemies
Destroy 5e7 Enemies
Clear EVERY sector (a,b,c) up to and including 15 within 20 minutes
Starting at sector 13, clear EVERY sector (a,b,c) up to and including 29 within 25 minutes
Starting at sector 26, Clear EVERY sector (a,b,c) up to and including 44 within 36 minutes
Starting at sector 39, clear EVERY sector (a,b,c) up to and including 59 within 42 minutes
Reach 1e21 Compute Levels
Reach 1e27 Compute Levels
Make all synth T6 recipes infinite
Make all synth T7 recipes infinite
Make all synth T8 recipes infinite
Max Out 32 Unique Void Shards
Sustain 1,792 Power Boost levels for 5+ minutes
Complete 20 Challenges
Gain 10,000 Total Crew Levels
Gain 1e6 Total Crew Levels
Reach Sector 69
Reach Sector 80
Gain 1e75 Research
Clear 102 Unique Sectors
Max Out 47 Unique Void Shards
Make all synth T9 recipes infinite
Make all synth T10 recipes infinite
Make all synth T11 recipes infinite
In a single prestige, starting at sector 1, clear EVERY sector (a,b,c) up to and including 74, within 74 minutes of prestiging.
Gain 5e6 Total Crew Levels
Complete 10000 Warps
Reach sector 74 and complete all tasks
Disable a capital ship 1000 times
Disable a capital ship 10000 times
Disable a capital ship 1e5 times
Break a capital ship part 2000 times
Break a capital ship part 50000 times
Break a capital ship part 5e5 times
Lose a fighter 50 times
Lose a fighter 500 times
Lose a fighter 5000 times
Lose a fighter 50000 times
Tier up Compute 5 times in a run
Tier up Compute 20 times in a run
Tier up Compute 100 times in a run
Gain 1e12 Capital Research
Gain 1e25 Capital Research
Tier up Overdrive 8 times in a Reinforce
Tier up Overdrive 16 times in a Reinforce
Tier up Overdrive 32 times in a Reinforce
Pull 10 enemies through the veil
Pull 1000 enemies through the veil
Pull 10000 enemies through the veil
Pull 5 rare enemies through the veil
Pull 50 rare enemies through the veil
Pull 1000 rare enemies through the veil
Gain 10 levels of Specimen Research
Gain 250 levels of Specimen Research