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