Just demonstrating how to collect all coins in area 13 in one run.
To make those coins appear you have to collect all bananas. Coins will appear at two locations per area right before flag 5 and 10.
Stamps: (Achievements)
1. Perfect through Area 2: get through area 2 without making any mistakes
2. Cutting Corners: the player must utilize a short cut. (probably skipping a flag?)
3. Skip 30 Bananas: Like the name implies. Try to jump over them or combine with stamp 2.
4. Double Damsel Rescue: the player must save Pauline twice.
5. Perfect Run: just complete the first two courses without crashing

I hope you don't mind that i have played the german version of Nintendo Land.
As a bonus you can enjoy my mega fail while trying to collect the last coins of area 3. ;)
Have fun!