Speak to Skylar again after completing Gone Fishin.' She's damaged her hand, and it's up to you to catch the Admiral. If you do, she'll generously split the prize with you.
Follow your marker to the Admiral's spot. This is a large area, and the game will warn you if you leave it, so pick a spot you like, but try to avoid fishing around other boats, which can cut your line.
There's no real trick to this- when you cast your line and get a bite, it'll always be the Admiral, which is convenient. The fishing minigame is the same as ever, just about six times longer than usual. You will definitely want to have the Fish King perk, and bait your hook with the Hybrid Sturgeon lure.
After that, it's just the battle. Keep up the pressure with your reel so as not to miss his few moments of weakness, and eventually he'll leap into your arms.
Return to Skylar for mission completion.
This victory unlocks the Wonderboy rod in stores. It makes every other fishing mission in the game extremely easy, and allows you to make hundreds of dollars in a few minutes, whenever you like.