Q:

Cut to the quick part

Bill the grave offender,
  venerable, form filler,
  leaving a paper trail,
  found on an old 3D tail,
  the fastest ending last,
  bucks the trend on April first?   

A:

I think the answer is

 HARE.

Bill the grave offender,

 This refers to William (Bill) Hare, one of the infamous Burke & Hare duo of criminals. "Grave" has a double meaning here, since IIRC they were grave robbers.

venerable, form filler, 

 Apparently the word "hare" can be used to mean "venerable", and a hare's home is called a "form". Thanks to @MOehm for help with this clue.

leaving a paper trail,

 In the outdoor game of Paper Chase, the designated "hare" leaves a paper trail to be followed by the "hounds".

found on an old 3D tail,

 A hare appears on the "tails" side of an old 3d coin. Thanks @Tom (the OP) for help with this clue.

the fastest ending last,

 In the fable of the Hare and the Tortoise, the hare is faster but finishes last in the race.

bucks the trend on April first?

 Male hares are called "bucks", and the stereotypical mad March hare differs from humans in becoming normal on 1st of April.

