Regulated 3.3V from a Lithium-ion (or LiPo) battery
You should try with BUCK-BOOST DC/DC converter. There are available with efficiency above 90%
Check out TI and Linear websites; there are "calculators" that would help you:


http://www.ti.com/lsds/ti/analog/powermanagement/power_portal.page
http://parametric.linear.com/buck-boost_regulator


Options:


TPS63031
TPS63001