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