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