Getting them unlocked is a bit tricky. It involves a mechanic called Fog. You can turn the fog on and off by talking to a special NPC in Fallgrim Tower - but it won't appear until after a certain point in the story. If you're curious about when you can start opening these unique chests, check out the full guide below for the short (and long) answer.
To unlock the strange fish statue chests in Fallgrim, you will need to acquire the [[Nectar Tar] key element of one of the three temple leaders. Earning the Nektar will cause a green fog to spill over into Fallgrim, and make those strange chests accessible.
Chests are filled with useful items - including key items needed to upgrade your weapons. Right outside Fallgrim's front door, there is a fish chest with a Quench acid you can use to upgrade your weapons.
Return of Nektar to the Old prisoner in Fallgrim Tower will clear the fog. You can summon him again by talking to Thesus on the second floor of Fallgrim Tower. It costs 1 preview to summon the fog again, or 1 preview to dispel the fog. You can switch between the two states as often as you like.
The fog is both a blessing and a curse. Ghouls are everywhere in the fog, but these enemies are only slightly more difficult than the bandits that normally inhabit the area. Look for two new Grisha mini-bosses that appear in the fog.
You can reappear indefinitely by disabling and then resetting the fog. The Grisha drop 6 glimpses each, so you can quickly farm for 25 ~ or more by beating them over and over. You will earn 10 (minus -2 previews for Tresus) each cycle.
Look carefully. There are fish chests everywhere in Fallgrim, and they become inaccessible if you clear the fog. I recommend going through and completely cleaning the area to catch any chests you might have missed the first time around.