Here is the full list of all 18 The Big Elk achievements.
Collect ten rockets!
Find the Yellow Ball!
Zone X must be completed!
Find and destroy the fake cow!
Find the Golden Crown!
Zone IX must be completed!
Zone VIII must be completed!
Zone VII must be completed!
Zone VI must be completed!
Zone V must be completed!
Collect ten cakes!
Zone IV must be completed!
Zone III must be completed!
Find and destroy ten geese!
Zone II must be completed!
Beat the slot machine!
Find and destroy the red button!
Zone I must be completed!