If you are talking a 2 ft level change - even if it's cut 1 ft, fill 1 ft, it's serious civil engineering machinery territory. There are lots of big boys toys hire shops if you want to try DIY - an excavator with backfill dozer blade and a dumper truck would be the minimum kit but it would be slow & messy.
A professional outfit would be the choice if you have the money, and preferably if they are going through a slack period and need the work. Otherwise you'll mainly be competing with people who have taxpayer's money to burn.
Points to note - specify that the turf & topsoil must be stripped & stored separately for replacement after levelling - it's the subsoil you need to move to the low ground, not the topsoil or the grass will never grow properly again.
Compaction of the fill also needs careful specification. All the laser levelling gear in the world is useless if the filled area is left loose as it will settle severely over 12 months or so. A guarantee that the company will come back to rectify any settlement would be good.
Enjoy!