Here is the full list of all 60 Jagged Alliance - there are Back in Action achievements.
Recruit Carlos
Stop Dr. Pippin's evil scheme
Recruit Dr. Vince
Recruit Hamous
Help Fatima and her children
Liberate Grumm City
Recruit Dimitri
Buy goods for 1,000,000$ in the online shop
Recruit Miguel
Recruit Iggy
Liberate San Mona
Recruit Maddog
Recruit Conrad
Recruit Shank
Liberate Balime City
Destroy a tank with the rocket launcher
Recruit Devin
Kill a total of 1000 enemies
Open 10 doors with the crowbar
Kill 100 enemies with melee attacks
Plant 100 mines
Kill an enemy with a mine you planted
Plant a mine
Throw 100 grenades
Use either smoke, stun, frag and teargas grenades at least once
Recruit 100 locals for the militia across several playthroughs
Miguel Cordona becomes king
Kill Deidranna
Kill Deidranna within 15 days
Kill Deidranna in tactical mode
Kill Deidranna in high difficulty mode
Liberate Meduna City
Liberate Alma City
Fire a total of 5000 bullets
Pick 10 locks
Kill an enemy with a frag grenade
Hire a total of 6 mercs
Liberate Cambria City
Recruit Ira
Restore 1000 durability on weapons
Recruit a local for the militia
Kill an enemy with a melee attack
Rescue a merc from dying
A single merc received over 100 damage in a single encounter without dying
Loot over 1000$ across several playthroughs
Secure Drassen Airport
Defuse a mine
Use explosives to blast a hole into a wall
Blast through 100 walls
Restore 1000 health
Loot over 100000$ across several playthroughs
Help Richie "The Wizard" Parker find a limited edition of DaHonko Flakes!
Kill Rygor Manson and save John Gaiden
Find the two dropped crates containing the equipment
Recruit Jamirez
Kill all five agents who have the missile launchers
Defeat Silevic and stop the missile launch!
Free Fox from captivity!
Find the dropped crates containing the equipment
Kill 10 enemies using the knife