2004 Pontiac Bonneville 3.8L drives great but if accelerate too fast cuts off

Possible fuel pump. Running out of pressure, gas. Check fuel pump pressure to verify.

Agree,all so check ya fuel filter.

have the injectors tested as well.

Could also be a plugged catalytic converter although that doesn't usually make the car stall. Check the trouble codes. You will probably find some clues there. I had similar symptoms with an older Bonneville. It was throwing all kinds of codes and the mechanic felt the ECM was failing. I found if I drove it gently it would run fine. The car was pretty well miled out by then and got wrecked that winter so I never had to fix it.

Ok Here's what already been done...Fuel Pump, ECM, Cat, TP Sensor, MAF Sensor. There were no codes, after new ECM, it only threw out a O2 sensor, which led me to believe Cat clogged, replaced CAT...still same issue drives fine with a slow acceleration, a hard acceleration or quick acceleration, vehicle backfires & cuts off but starts right back up

Has the timing ben checked?

ok. Could be timing but now thinking bent or burnt valves may be the culprit, not sure. Think that there in lays the problem!! Will let you know!!

That motor has a timing chain, not likely to have jumped time. To verify this and bad valves just do a compression test.