“Loud as possible”
Ok. Go to the pound shop and buy a personal attack alarm. Break it open and use the sounder in that complete with its resonance chamber. There will also be a flyback inductor. Use that (or make your own) like this:
One end of inductor connected to 12v, the other end connected to power transistor collector. Transistors emitter to ground (common with Picaxe), and base to Picaxe through 330R resistor. Connect the Piezo from ground to collector.
When the Picaxe signal goes high, the collector goes low and 12v is put across the inductor, charging it’s magnetic field. When the Picaxe signal goes low, the transistor switches off and the back EMF on the inductor shoots the voltage on the collector to many times 12v. Keep the duty cycle low, maybe 10% or so. A ‘scope will help you tune that.
Use a transistor that can cope with high collector voltages. There will probably be one inside the personal alarm.
It will be very loud.