There are a total of 19 secret shells in the game: 3 per chapter (except chapter 5) and 1 in the credits. They do not have to be obtained in the same playthrough. However, there is no way to find out which ones you are missing, so I recommend you collect them all at once.
Maka91 has made a perfect guide for the game which shows you all of the collectibles and achievements. So if the video helps you, be sure to give Maka a thumbs up on YouTube. You can complete the whole game with the guide, but if you are only looking for the shells, I have listed the time stamps below.
Time stamps for the shells:
Chapter 1: 3:54 / 6:05 / 10:29
Chapter 2: 13:58 / 16:15 / 21:10
Chapter 3: 23:32 / 28:17 / 31:07
Chapter 4: 36:37 / 40:38 / 41:00
Chapter 6: 52:14 / 52:52 / 59:12
Chapter 7: 1:06:48 / 1:11:13 / 1:11:44