Reel in 60 types of fish with the any fishing rod you choose. Jourdenaux quote: "First, I'll need you to reel in a large variety of fish. Let's see...yes, 60 different species will work. I leave it to you to choose which rod to employ."
Any fish you have already fished up since Fisherman's Heart was added to the game count. If you have already done 60+, he will continue onto the next step automatically.
Speaking to Jourdenaux again after fulfilling this requirement will unlock a new category of Records of Eminence objectives, Fishing > Fishing (Tenacity).
Complete all of the trials listed under this new category. All of the trials require the use of Lu Shang's Fishing Rod to complete.
For fishing trials that require X amount of catches, catching multiple fish at once with a single cast using certain lures (such as the Sabiki Rig) will have each fish caught count toward progressing the trial.
Upon completion of the trials, return to Jourdenaux and relinquish your Lu Shang's Fishing Rod to him, who will reward you with the Lu Shang's Fishing Rod +1. It will be tagged with your server name, and a number indicating how many other players on your server have completed the quest and obtained the rod before you.
Note that the original Lu Shang's Fishing Rod is lost in this process, and that the +1 rod is untradeable and unsellable to other players. The rod is otherwise identical to the original version, including the possibility of breaking it with the broken version also being Rare/Ex. Jourdenaux is able to fix the rod if you trade it to him along with an Ancient Lumber. The rod may also be repaired through Woodworking as with the original Lu Shang rod, but this will cause it to temporarily lose its server/number tag. Jourdenaux is able to restore the tag for you.
Highest Fish Levels by Region
For people that are leveling their fishing skill during this quest, here is a suggested list of each region's highest level, safe fish in ascending order in order to finish the regional objectives while still leveling. Keep in mind that Lu Shang's Fishing Rod gives poor skill up rates before level 50.
Lu Shang's fishing rod has a hidden power deep inside, which Jordenaux has offered to draw forth if he deems you worthy--by collecting 60 types of fish and fulfilling all Records of Eminence objectives in the "Fishing (Tenacity)" category.
SPOILER WARNING: Click here for additional details about this story line.