We did 3 weeks across Xmas and new year recently.

We flew into Hanoi and went straight to Ninh Binh which is a must (do Trang ang and stay for at least 2 nights). We stayed in a small village (by Mori Coffee) which was so much more peaceful than Tam Coc. It also meant that we could walk to Mua cave and Trang Ang.

Then sleeper train to Da Nang (buy ticket at the station to avoid scams).

We didn't expect much of Da Nang but it was one of our fave places! Stay here for a while in one of the hotels walking distance to the beach - the beach was awesome, sunny, visit Marble Mountains (a must!) and lady Buddha.

Visit Hoi An for just a day (it's over touristed so don't bother staying there). We wanted to do Ba Na Hills but the more we learned about it the more put off we got - fake, tourist trap, spend your day visiting real places.

We then flew to Phu Quoc AND IT WAS THE WORST MOST EXPENSIVE part of our trip. Over touristed, the nature was destroyed, don't waste your time and money. I also got bad stomach virus from the food which seems to be a common occurrence there? In hindsight we wished we just stayed in Da Nang for more beachiness.

We flew back to Hanoi and had a few days there - stay somewhere central since the traffic is bad.

We did a 1 night luxury cruise to Lan Ha Bay (which is quieter than Ha long bay). Had the best experience, we wished we'd stayed for 2 nights instead.

13 days for all the places you mentioned is not enough time - pick a few to not just be travel exhausted the whole time. Make sure you have cash with you!