For those wondering,

double triple - six patties
bossy - all beef
deluxe - with everything (lettuce, onions, tomato, etc)
on a raft - on toast
4x4 - 4 patty by 4 cheese, so (6x4) 24 patties and 24 slices of cheese
animal-style - cooked in mustard
extra shingles - extra toast
with a shimmy - jelly on the toast
and a squeeze - orange juice on the side
light axle grease - with butter
make it cry - extra onions
burn it - well done
let it swim - extra sauce

You forgot the orange juice on the side