Earth Auger You Need This

Throw away your hoe, your claw, your compost turning fork and get one of these

Its a bulb planter, or earth auger, depending on the brand you find.  I bot my at Homerville, they sell it as a bulb planter, manufacturer is Ames, cost was less than $20.  You can find them all over the web, 24" is the perfect length IMO.

I mount mine in my cordless drill, set on low.  Screw it in, pull it out.  Repeat.  You can turn a bed over in stages if the bed is a little hard- 3 inches or so deep, make a few passes, the go over the same area and go deeper.  I suppose you could end up cultivating 24' deep- I don't generally go that far.  Works great to mix the compost you should be making in trash cans, too.  If you have long grassy stemmy stuff in your compost it will tangle around the shaft, bit of a pain in the butt.  Gotta find a way to chop or grind my compost fodder.

You could use a corded drill too.

Or if you want the old fashioned manual labor experience, find on of these:

The hand powered auger might actually work better in the compost barrel as far as snarling the long stem stuff around the shaft.  I'll try that this year.

Confession:  OK, I didn't really throw away my other tools, they just get used less.  A lot less.