You will need to change not only the complete engine but the airbox, MAF, intake manifold, exhaust, injectors, throttle body, intake boots, gearbox, clutch/flywheel, propshaft, diff, 330i front and rear brakes, 330i rear trailing arms ect. As already stated, cost wise its much cheaper to buy a 330i with all the right bits to begin with...
You can use your existing engine mounts, wiring harness, headers, sump, alternator, cooling system parts, oil filter housing and all the other bits that bolt onto the block as both the 320i and 330i use the M54 motor. The 320i head has 3mm smaller valves than the 330i head yet they share the same exhaust cam, intake cams are different with the 330i one having more lift.
Your original 320i ECU will run the 330i motor in standard form, its the same ECU for both cars but to get the most out of it have the 320i eprom chip replaced with a 330i eprom chip.