Here is the full list of all 21 Incremental Adventures achievements.
Reach floor e100
Prestige on layer 100
Ascend on layer 5
Complete 25 ascension trials
Ascend on layer 4
Prestige on layer 50
Ascend on layer 3
Complete ten ascension trials
Ascend on layer 2
Complete five ascension trials
Complete an ascension trial
Reach floor e10
Prestige on layer 20
Ascend for the first time
Prestige on layer 10
Reach floor 1000
Prestige on layer 5
Reach floor 100
Prestige on layer 2
Prestige for the first time
Reach floor 10