Quick answer: Cupid's Wings is a crafting ingredient obtained by catching a Roseveil Koi in the Behind Waterfall area and showing it to Sweetheart Sam after completing earlier duo quests.
Cupid's Wings is one of four key materials needed to craft the Cupid's Embrace fishing rod during the Valentides event in Fisch. The item is locked behind a multi-stage questline that requires a duo partner and involves catching several event-exclusive fish across Valentine Island.

Requirements Before Starting
You must form a duo with another player before beginning the Sweetheart Sam questline. Travel to Valentine Island and open the duo menu by clicking the handshake icon in the bottom left corner of the screen. Select a player and send a duo request. Once accepted, both players will see "Valentides Duo" status.
The duo partnership is mandatory for all steps tied to Cupid's Wings. Solo players cannot progress past the initial NPC dialogue.

Complete Sweetheart Sam Quest 1
Locate Sweetheart Sam near the central fountain on Valentine Island. Interact with him and select the "Duo Quest!" dialogue option. He will assign the first task: catch three limited Valentine event fish.
Fish anywhere around Valentine Island with your duo partner until the quest tracker shows 3/3 limited fish caught. Return to Sam and turn in the quest to unlock the next stage.

Complete Sweetheart Sam Quest 2
Sam's second quest requires 50% completion of the Valentides 2 Bestiary. Open the Bestiary menu, navigate to the Valentides 2 tab, and check the progress bar at the bottom. Continue catching event fish until the bar reaches at least 50%.

You must also catch the Secret Dove fish. Both you and your duo partner need to sit on the white bench under the heart archway at the top of the hill on Valentine Island. After a short wait, the lake water below will turn pink. Go down to the pink lake and fish until you catch the Secret Dove (Mythical rarity).

Return to Sam with the Dove to complete Quest 2.
Complete Sweetheart Sam Quest 3
After turning in the Secret Dove, Sam will assign Quest 3: catch 10 Lovestorm fish. Lovestorm is a timed event that spawns every two hours in the main ocean near Moosewood. A server-wide notification will announce when the event begins.
When Lovestorm starts, travel to the purple-tinted water and catch 10 limited fish. You must also catch a Lovestorm Turtle during this event. Do not sell the turtle—it is required for the next step.
Return to Sam after catching 10 Lovestorm fish. He will reward you with 750 Chocolates and ask if you noticed anything unusual during the event. Select the dialogue option "The odd looking turtle." While holding the Lovestorm Turtle in your hand, speak to Sam again to receive Cupid's Core.

Unlock Cupid's Wings Hint
After obtaining Cupid's Core, interact with Sam again and select "Secret Hints?". Choose "Hint 1" and pay 50 Chocolates. Sam will give a clue: "Beyond the Waterfall."
This hint directs you to the Behind Waterfall area, a cave entrance located behind a waterfall on Valentine Island. Enter the cave with your duo partner and sit on the bench on the left side. After sitting together, a pink pool will appear in the water.

Catch the Roseveil Koi
With the pink pool active, cast your fishing line into the water inside the Behind Waterfall area. The Roseveil Koi (Legendary rarity) can only be caught when the pink pool is present. Use Fischversation Hearts or Chocolate Fish as bait. The weather must be Foggy, and the season must be Winter.
If the pink pool does not spawn, ensure both you and your duo partner are sitting on the bench simultaneously. Once you catch the Roseveil Koi, return to Sweetheart Sam.

Receive Cupid's Wings
Show the Roseveil Koi to Sweetheart Sam. He will take the fish and reward you with Cupid's Wings. This item is one of four materials needed to craft the Cupid's Embrace rod at the Ancient Archives.
The other three materials are Cupid's Handle (obtained by catching the Love Letter Long Pike at the Wishing Well), Cupid's Core (obtained by showing the Lovestorm Turtle to Sam), and a Sweet Lovestorm Turtle (obtained by catching a Lovestorm Turtle with the Sweet mutation). You will also need 15,000 C$ to complete the crafting process.

Verification
After receiving Cupid's Wings, check your inventory to confirm the item is present. The item icon will display a pair of pink wings. If the item does not appear, ensure you completed all prior quests in the correct order and that your duo partner was active during the Roseveil Koi catch.
If the pink pool does not spawn in the Behind Waterfall area, exit the cave and re-enter with your duo partner. Both players must sit on the bench at the same time for the pool to activate.
Cupid's Wings is a time-limited item tied to the Valentides event. The questline and all related fish are only available during the event window. Once you have all four crafting materials, travel to the Ancient Archives on Ancient Isle and use the Crafting Anvil to create the Cupid's Embrace rod.