The challenge was to build a Standard deck under $20 (mid) using Felidar Sovereign's triggered ability as its primary win condition. This deck is $19.62 at publication on 2016-04-21.
Felidar Sovereign has several problems:
1. It is vulnerable to normal non-damage removal.
2. It can't be cheated into play at end of opponent turn.
3. It is expensive to cast or reanimate.
The win condition brings its own challenges:
4. Some of the most efficient life gain spells, like Feed the Clan, just rotated out.
5. Other good life enhancers like Alhammaret's Archive don't do anything on their own.
6. Many good cards for this deck are just too expensive ($) or more likely to kill the opponent before you gain enough life.
7. It is really important to play defense -- especially if you lose any life early, it's going to have to be a long game if you expect to win.
So I went with extremely defensive cards and used Ayli, Eternal Pilgrim as the primary means of gaining life. If you can keep Ayli alive, you have a good shot at winning as the game goes longer.
All 4 color pairs with white had some possible strategies, as did mono white. I didn't explore triads much (Abzan or Esper in particular had some interesting possibilities) because the mana bases are difficult on budget. There are some reasonably good colorless ramp spells available, but in the end I felt like the plan is stronger if you are using spells for other things. Getting Sovereign out early isn't generally a priority.
The basic plan here is to use your walls and skeletons to block, but sacrifice them to Ayli if they are going to die. When you have 30 life, she can start exiling things. At 40 life, if your opponent doesn't have removal waiting (or you are holding several Sovereigns), put out the Sovereign.
First game the opponent probably won't know what you're doing, but second game they will try to hold removal for your two most important creatures, so depending on their deck, sideboarding in Vessel of Malignity might help.
Card by card:
Fortified Rampart and Guardians of Meletis, with Spidersilk Net - two responsibilities, protect you from attack and gain you 6 - 8 life. If the opponent is too strong in the air, Orator of Ojutai can replace some of these. The reason I used Guardians instead of Wall of Resurgence is that you need your lands to stay alive (i might be wrong on this choice, and the Wall of Resurgence is definitely better in certain situations). Normally you would want to play walls before Ayli.
Sanitarium Skeleton - recursive blocker, with huge benefits once Ayli can start using it io exile cards. Feel free to cast early and block liberally. If you survive to high mana, it becomes very powerful. You might not need all 4 since they become redundant in the late game.
Ayli - I think you know why she's here. 4 copies because you can't really win without her. Don't forget about the deathtouch if you need to stop a really nasty attacker. Note that if you want Sovereign to trigger at your upkeep, you have to have 40 life when your upkeep begins, meaning any needed life gains should be done at end of opponent turn. If Sovereign triggers and then you get knocked below 40 life before it resolves, you can use her to get back up (even sacrificing Sovereign itself).
Felidar Sovereign - not much to add here. Lifelink is worth remembering.
Dazzling Reflection and Encircling Fissure - to save your life total and gain you life, especially if your board is in bad shape. These are mainly to buy you time. Dazzling Reflection can also be used just for life gain if needed.
Planar Outburst - the magic reset button. Try to gain card advantage with this, and also try to sacrifice any creatures for value before casting it.
Ever After - this gets back whatever you need (even if it's two walls), with the side benefit of preventing you from getting decked. In a long game or against a controlling opponent, your library should be able to outlast anything other than dedicated mill strategies.
Sideboard cards should include something to protect your best creatures (the sideboard above is just stuff I was playing around with). Most effects like this cost at least 3 mana, so I'd go with Eerie Interlude, which can save your Sovereign from almost anything if you hold it until you have 9 mana. For opponents with wide strategies, Virulent Plague or Rising Miasma/Biting Rain (Flaying Tendrils shreds your skeletons). For really bad creatures, Immolating Glare or Celestial Flare.
This deck will have trouble with decks that control using lots of removal or counterspells, and decks with must-kill creatures (especially big fliers or unblockable).
To upgrade the deck, Caves of Koilos would probably be good (the life loss is minor) and Shambling Vent would definitely be good.