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