Here is the full list of all 25 POSTAL Redux achievements. It takes around 12-15 hours to unlock all of the achievements on Windows.
Complete every level in Co-op mode.
Perfect all Rampage levels.
Complete the Campaign having killed only hostiles.
Complete the Campaign with a total play time of 30:00 or less.
Complete all Rampage levels.
Complete the Excess Postage campaign in Nightmare difficulty.
Execute two of every hostile type.
Firebomb the Marching Band.
Kill 30 people with the Napalm Launcher.
Earn a kill with every weapon.
Finish a level with less than 10 health.
Commit suicide.
Watch the entire credit sequence.
Complete the Campaign.
Complete the Campaign having left no survivors.
Kill four or more people with a single Rocket Launcher missile.
Wipe out the game protestors in Ghetto.
Kill all Ostriches in The Farm.
Blow up 50 barrels.
Kill three or more people with a single Mine explosive.
Duck under 10 rockets.
Reach the half way mark of the Campaign.
When burning, set someone else on fire by running into them.
Perform 13 executions.
Make your first kill.