Selecting the right battery type and capacity
You can see from the comments that your only potential option is from the lithium chemistry. The lead acid is just way too heavy and probably too bulky as well. 

265Wh/Kg is quoted for lithium.  This is correct, but also more of an accepted 'potential' value and not necessarily what you will get given your specific needs. For example your need for a relatively high current might require a lithium battery that is constructed slightly differently giving you a lower capacity per kilogram.

Let's look at what you can get in the real world. The LiMn battery that powers the Nissan Leaf will handle your compressor.  With a little rearrangement of the cells you could make it into a 12.6 volt 60 Ah battery that weighs exactly 12 lbs (5.5kg). It would give a nominal 684 Wh and can supply as high as 240 amps! Note that this lithium battery doesn't come close to the example given by Russel McMahon!

Depending on your compressor's duty cycle, this might work for the 10 hours, or it might only give you 3 hours. You will easily get the 100 cycles you asked for even if your depth of discharge is 90%. .

This battery could be purchased for about $160 or so.