Here is the full list of all 18 The Big Elk achievements.
Beat the slot machine!
Find and destroy the red button!
Zone I must be completed!
Zone II 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!
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!