Here is the full list of all 21 Skyshine's BEDLAM achievements.
Win a battle against 15+ enemies
10 Battle win streak!
Blast 10 enemies with The Nuker!
5 Battle win streak
3 Battle win streak
Reached Aztec City
100 or more kills
Reach Bysantine during a Double Down!
Obtain 3000 Crude
Obtain 3000 Meat
Obtain 200 or more Power Cells
Visit 40 or more POIs
Visit 35 or more Side POIs
Reach Bysantine during Double Down on Bedlam difficulty
Obtain over 3000 passengers
Reach Aztec City with over 1800 passengers
Score at least 500,000 points
Score at least 1 million points
Score at least 2 million points
Score at least 4 million points
Score at least 6 million points