Unless you need a feedback loop for the micro to know how loud it is, or change it with a very wide dynamic range or something, once you can generate the sound at any level, the loudness has nothing to do with the micro.
You just need more in the amplification stage and a suitable speaker. I assume this is for a device with a built in speaker and not connecting to an external system? Do you need the micro to be able to control gain? Do you have much of a physical space requirement? Power requirements? Sound quality requirements (also what kind of sound is it)?
You can get 90dB up close with a small, cheap 8 ohm speaker and a single power transistor, though you'd probably need a second as a preamp stage and it's not going to sound great. If you want 90dB several meters away, then you're going to need a lot more driving power. There are a number of single chip amps that make it fairly easy (just follow the app note, for example), but without knowing the physical constraints of the device and the area that it needs to be heard... it's really tough to try and recommend specifics.