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