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