Castaway Paradise

Since shells only spawn when a new day starts in game, you can use this trick to advance the game day and get them to spawn again. It's still luck based as to what shells appear but this way you won't have to boot the game up every day until you get them all. You can go to the museum and press A on empty exhibit spots to see what your needed items look like.

In order to advance the game you need to boot the game twice, the second time with your console clock registering as one day after the first. You can do this by adjusting your console time zone.

Note: The steps given are for if you go back a day and then to the present day, triggering the date change in-game. Depending on your time zone you may have to go forward a day, then to the present day, and repeat. The basic idea is the same, you just need to boot the game twice with a forward day change in between.

Step 1: Press the guide button and go to the System tab. Then select Settings > System > Time
Step 2: Adjust your time zone so you go back 1 day. Example: If your current time is 1:00AM (-5:00 timezone), you can adjust your timezone to the -7:00 timezone so the time will be 11:00PM the day before.
Step 3: Boot the game and load into your house. Close the game, and repeat Steps 1 and 2, but this time going back to your previous timezone (or anything in your current day).
Step 4: Boot the game again. If done correctly the game will have gone forward a day and spawned shells, trash, cobwebs, etc. Now you can check for any shells you need.

Even if you don't see the shells you need, you may want to pick everything up off the beach because the game has a limit as to how many items can be present and they will start to add up. You can save time by opening the quick inventory (Y) and moving the cursor around the map - you can pick up any dropped items in this mode by pressing B. The only snag is you can't cross water or bridges in this mode so you will have to move across those yourself, but otherwise you can grab everything much quicker.

Needed shells for this achievement:
Blue Sunray Venus
Brown Cone
Brown Razor Clam
Brown Shark Eye
Brown Tiger Cowry
Checkered Cone
Flamed Auger
Green Banded Tulip
Green Shinbone Tibia
King's Crown
Lilac Auger
Nautilus
Noble Murex
Orange Auger
Orange Banded Tulip
Orange Calico Scallop
Orange Silken Scallop
Oyster
Pink Ribbed Drill
Pink Shark Eye
Pink Sunray Venus
Precious Wentletrap
Prickly Drupe (pink)
Prickly Drupe (yellow)
Purple Calico Scallop
Purple Tiger Cowry
Venus Comb
White Razor Clam
Yellow Cone
Yellow Ribbed Drill
Yellow Shinbone Tibia
Yellow Silken Scallop