Here is the full list of all 19 War in a Box: Paper Tanks achievements.
Built 25 HEAVY-GUNS
Finish the level with 1 life
Granted for first kill
Built 25 ARTILLERY
Built 100 CANNONS
Built 25 FLACKS
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
Lose 3 rounds in a row
Win 10 rounds in a row