As audioguru said, you need to decide where you want to do the step-up to 220v:
Either use a high-frequency transformer to generate a high-voltage (350v ish) DC, and then use a PWM amplifier to generate a 220v AC from that,
OR
Use a low voltage PWM amplifier to generate a line-frequency (50Hz or whatever) sine wave at your battery voltage, and then step this up using a line frequency transformer.
Of these two, I'd go with the second unless you have good reason to do otherwise. It should be safer, if nothing else.
Ignore the power transformer for a start, and begin by building a high-current PWM amplifier. You could control it directly from the microcontroller since you have one available. A driver IC like the IRF2011 would be a good place to start.