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