No. You only need A-levels to start ACCA. Anything higher than A-levels will provide you with exemptions. A levels will not provide you with any exemptions, so you would have to start from F1 to P7 (14 papers). Diploma would most probably help you to 4 exemptions, ie. you would start from F5 to P7.

However, note that you can just take 6 months to complete these 4 papers compared to Diploma which takes more than 2 years just to get the 4 paper exemption.

But since you are doing through the Diploma route, then the A-levels or CAT route is out of the question.

I would say that having a degree from NTU then completing ACCA and going straight into ACCA with the Diploma in hand both brings you into the same path, but NTU would probably provide a faster path.

ACCA teaches all the basics. No worries about that.

Note that this is only my OPINION. NTU is quite a prestigious university, therefore career paths would most likely be better than an ACCA fresh graduate since wherever you go to (most likely tuition centres, again I would assume you will be studying ACCA at Singapore, and I only know Kaplan, BPP and SAA) does not have such career services provided by NTU.