Here is the full list of all 19 War in a Box: Paper Tanks achievements.
Granted for first kill
Built 25 ARTILLERY
Built 100 CANNONS
Built 25 FLACKS
Built 25 HEAVY-GUNS
Built 20 TESLAS
Destroy 300 units using ARTILLERY
Destroy 1000 units using CANNON
Destroy 1000 units using FLACK
Destroy 300 units using HEAVY-GUN
Destroy 50 units using TESLA
Collect 35 stars
Collect 50 stars
Collect 65 stars
Finish the game in Expert mode
Kill heavy tank or zeppelin with HEAVY-GUN
Finish the level with 1 life
Lose 3 rounds in a row
Win 10 rounds in a row