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