Here is the full list of all 22 Heavy Memories achievements.
Complete the story without death
Crush 500 humans with your tank
Destroy 500 enemy tanks
Explode 1000 barrels
Complete the story on middle tank
Complete the story on heavy tank
Complete the story on light tank
Complete the story on mammoth tank
Destroy every breakable wall at military training
Don't get hit while holding positions
Destroy all enemy tanks and people on enemy base assault mission
Rescue all civilians instead of killing them
Don't touch grass in retreat mission
Escape enemy base without triggering any alarm
Defend your base without power-ups
Destroy at least 50 enemy tanks in the bridge battle
Escape the bridge without repairing
Get 9 lives on the counter
Kill 100 rocket-men with their rockets
Get all bonuses at the same time with maximal extra health
Shoot down 100 enemy bullets
Explode yourself on at least 100 land mines