Here is the full list of all 48 Chaos Chain achievements.
View the tutorial.
Play Chaos Chain.
Complete "Eviction Notice".
Enter Slade City.
Complete "Problems at Home".
Complete "Something in the Basement".
Meet Lynch for the first time.
Complete "Slipping Away".
Complete "Rats Nest".
Complete "Words of Gold".
Gamble by playing a game of "Verge".
Complete "Family Comes First".
Complete "Dead Drop".
Get your first CyWare installed.
Complete "Shady Dealings".
Reach 25 total (+/-) reputation or more.
Have Drako as a follower.
Complete "The Catch".
Complete "Closed Circuit" at least once. (Repeatable)
Read a data item.
Get your first BiWare installed.
Complete "The Edge".
Eat some delicious Street Ronin ramen noodles.
Complete "Stubborn Love".
Complete "Helping Hands".
Complete "Relief Recovery".
Complete "Working with Scraps" at least once. (Repeatable)
Force an enemy to retreat.
Have Cassia as a follower.
Complete "Repeated Robberies".
Sell data to an info broker.
Complete "Unwanted Guests".
Get a drone companion.
Complete "Precious Possession".
Fast travel by using the metro.
Complete "Keep the Dogs at Bay".
Complete "Eyes on the Inside".
Successfully breach a system through hacking.
Revive a fallen companion.
Have Jackal as a follower.
Have Chronic as a follower.
Reach at least 5 heat.
Pay a fixer to lower your heat.
Reach 10 heat.
Complete "Dirty Rotten".
Use a memory chip to save progress.
Complete "A Real Meal".
Travel between two districts (or subdistricts) on foot.