Simultaneous audio

Hello I currently have an arduino based game that revolves around GPS with Bluetooth, infrared, sound u-disk module, buttons, leds and runs off a li-po.
I won't get into game mechanics but our game plays effects based on game factors however we recently decided we wanted it to play ambient sounds aswell and because we have rf we can stream audio across it for player announcements.

A good example of this is in modern computer games where there is music from the fame, effects from guns or whatever and whole game announcements think team fortress 2 or even modern warfare.

I realise that is not a fair comparison so a Nintendo ds is a microcontroller based device that does this for reference.

To paraphrase I am looking for a microcontroller based system that can play 2-3 simultaneous sounds with different start time either another microcontroller or external hardware.

Can an arduino accomplish this?
What external hardware is commonly used for this?
Avr or arm's as possible alternatives would be helpful.

I don't want to use a raspberry pi they take to long to boot you would have to write your own operating system or run it off raspian meaning no good for commercial production and there is no sleep mode or power saving.

I'm not hugely familiar with arms or avrs so any advice there for alternatives would be helpful, many thanks Chris.

Edit: I have looked at the Nintendo ds which is a perfect example of this and it uses the arm9 which is now replaced with a range of arm cortex models, ironically there is a arm cortex-3 in the arduino due that should mean it is more than capable however whether any additional hardware needs to be used is questionable.

Just noticed I slightly misunderstood what you're aiming at re: graphics. I only spotted the bit about a basic UI, not the full camera view. Forget that. Lol.