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