You have 3 minutes to recover the NPC's Penguin Ring, which is enough time to land 6-7 successful catches.
All "bites" have easily weakened stamina, can be caught with any bait, and have a 100% bite rate (unless you cancel your cast prematurely). Either a chest or a monster will be on the line.
Reel in your line if you get the item message "You feel something pulling at your line." A Jade Etui (a chest) appears on the beach after you reel in this catch. Click it once to open it, then hit your fishing macro immediately to resume fishing. Chests that are caught, as with any sort of "item" catches, do not consume bait.
If you do not have other party members or SMN pets available to hold enemies for you, it is recommended not to reel in your line if you get the monster message "Something clamps onto your line ferociously!" This is a Puffer Pugil. It has True Hearing, so Sneak will not prevent aggro from it.
Only one Puffer Pugil can be spawned from the event at a time. If it is fished up and kept alive, you will not hook any more monsters. This carries over between Brigand's Charts, so if a Puffer Pugil is kept alive from a previous chart, the next person to use a chart will not catch any Puffer Pugils, either.
You do not have to open the chests immediately, but it's recommended that you do; just make sure to immediately resume fishing after opening the chest. If done quickly enough, it will not detract from your fishing time. You can have multiple chests on the beach at the same time, but they vanish at the end of the three minutes.
When the NPC says that he's fading, you have about 10 seconds remaining. Immediately pull in your line and open any chests on the beach (if any) at this point.
The Penguin Ring may be found in the 4th or 5th chest caught. However, even if you manage to get all 5 possible chests, you are still not guaranteed to get the ring.
When the time is up, the NPC and any remaining chests vanish and the Level Restriction effect is removed. The loot obtained remains in the Treasure Pool for the usual time if there are additional party members present or if your inventory was full.