This quest is known to cause mayn troubles, if you're bitten by the Bug you can only reload a old save or try to fix it via console.

But before doing anything, make sure it's the Bug


You visited all islands and killed all Garygoyles&Eggs?

Caldera - No Gargoyles
Isle of the Dead - No Gargoyles
Tacarigua - 3 x Gargoyles and 3 x eggs.
Upon arrival and talking to Eldric the sub-quests 'Gargoyles on Tacarigua' and 'The Brood on Tacarigua' will begin. Speak to Booze in the bar and he will tell you where they are and even mark them on your map. Press and navigate to your logbook and press on either of the two quests to activate their locations on your map. They are located on the beach to the North West of the Pirates Den. Once both sub-quests are completed return to your ship and speak to Eldric.
Maracai Bay - 6 x Gargoyles and 6 x eggs
Upon arrival and talking to Eldric, the sub-quests 'Gargoyles at Maraci Bay' and 'The Brood at Maracai Bay' will begin. Speak to Valdez and he will tell you there are two groups of Gargoyles to the South. Activate their location as per above. Each Gargoyle is surrounded by numerous Sand Devils so be sure to try and take them out first. Once you have completed both sub-quests return to your ship and speak to Eldric.
Sword Coast - 6 x Gargoyles and 6 x eggs
Upon arrival and talking to Eldric, the sub-quests 'Gargoyles on the Sword Coast' and 'The Brood on the Sword Coast' will begin. You will then need to speak to Chani, she will either be on your boat as a member of the crew if you progressed down the Voodoo path of the story, otherwise you will find her in the Shaganumbi Village. Once you have spoken to her the locations of the Gargoyles and eggs will appear on your mini-map, just be sure to activate the quest as per the above locations. The Gargoyles are located in two groups of three, the first of which is west of the Pirates' Tower and the second of which is south of the Pirates' Tower. The eggs are located in the same locations as the Gargoyles. Here the Gargoyles will be surrounded by either Cave Bats or Sand Devils.
Isle of Thieves - 3 x Gargoyles and 3 x eggs.
Upon arrival and talking to Eldric, the sub-quests 'Gargoyles on the isle of Thieves' and 'The Brood on the Isle of Thieves' will begin. You will then need to speak to Jaffar. He will be a member of your crew at this point in the game, so you will find him on the main deck of your ship. Once you have spoken to him, the locations of the Gargoyles and eggs will appear on your mini-map, just be sure to activate the quest in your logbook for them to appear on your in-game map under the Sea Chart tab in the pause menu. The Gargoyles and eggs are located to the South of the Gnomes Village. They are most easily accessible by taking the path into the jungle from the Southern beach, close to where you dock your ship at the island. The Gargoyles will be surrounded by numerous Sunken Ones, Caves Bats and Warrior Termites.

-One of the known problem is gargoyles not spawning...if this happend reload or console
-Another Problem is that the quest got stuck if you did not visited all islands, including the ones that don't have gargoyles, never had this problem myself, only read about it.
- the last common problem is caused by the players if they forgott to talk to eldric at every "new" island