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