Trophy Challenges are earned through a variety of gaming-related requirements.  Some trophies will present special rules which will define how a Challenge must be approached. 
These special rules are defined below and will be updated as new Challenges and requirements are introduced.

Rule: Complete the rules in the order listed to determine which trophy you receive
Related Challenge: The Chess Queen
What it means:  There are two variations of this trophy available: the Red Queen and the White Queen.  The requirements for each variation are the same, but the order you complete them in will determine which trophy you receive.  This includes all 5 rules for the trophy--playing three games and writing two reviews.  They must be done in the specific order listed on the Challenges page in order for you to win one of the Chess Queen trophies.  You can only win one of the Queens, either Red or White, so choose the order of the Queen you wish to receive. 

Rule: Own a Vampire Cape
Related Challenge: The Immortal
What it means:  Before starting this Challenge, you must own the "Vampire Cape" item, which can be purchased from the Avatar Shop within your Verizon Games player.  If you are not in possession of a "Vampire Cape," no credit will appear on this Challenge even if you play the required games.  Your avatar does not have to be wearing the cape--it just must exist in your "owned items."  To purchase the cape, visit your Community Home in the Games Player, click "edit" next to "My Avatar," and visit the Wardrobe Shop.  The Vampire Cape is available under the "Costumes" section.  (If you already own the cape, you do not have to buy it again!)

Rule: Spend 3,000 PPs
Related Challenge: Big Spender
What it means:  The special requirement for this Challenge requests that you spend 3,000 Prize Points in a single trip to the virtual Lounge Shop.  You don't have to buy a single item worth 3,000 PPs--for example, you could buy 30 items that each cost 100 PPs.  This just means that when you are checking out, the total in your cart on that trip must be equal to or greater than 3,000 PPs.  It also must be a trip to the Lounge Shop--furniture and goods for your Lounge itself--purchasing Avatar items, such as shirts and hairstyles, will not count for this particular trophy.

Rule: Pass the quiz
Related Challenge: Plants vs. Zombies
What it means:  This Challenge is completed not by playing for a certain amount of time, but for completing a quiz with questions about the game itself.  Extended details can be found in this FAQ entry.

Rule: Cameo Games
Related Challenge: Prime Time
What it means:  Two of the required games for this Challenge are merely cameos--they will only award credit on specific days.  You only need to complete the playtime for one of them to finish the task.  So, you can finish the "cameo" requirement by playing 2 hours of "The Apprentice" on Monday, Tuesday, Wednesday, or Thursday.  Or, you can also finish it by playing "Family Feud: Battle of the Sexes" on Friday, Saturday, or Sunday.  You can also play a little of each--if you played 1 hour of "The Apprentice" on Thursday, and 1 hour of "Family Feud: BotS" on Friday, you would receive the full 2 hour credit towards the cameo games.       

 
Rule: Prerequisite Challenge
Related Challenge: Around the Moon, Thanksgiving Feast, Fireside Gamer, Jewel Quest Heritage, Think Green
What it means:  Before starting on this Challenge, you must have won the Prerequisite Challenge listed. 

Around the World is the Prerequisite Challenge for Around the Moon; if you have not fully completed Around the World, you cannot earn any credit toward Around the Moon.

Cookin' Granny is the Prerequisite Challenge for Thanksgiving Feast.
Comfy Quilt is the Prerequisite Challenge for Fireside Gamer. 
Jewel Quest Ensemble is the Prerequisite Challenge for Jewel Quest Heritage.
Eco Warrior is the Prerequisite Challenge for Think Green.
April Showers is the Prerequisite Challenge for May Flowers.

Rule: Play the games in the order they are listed
Related Challenge: Harvest Fest, Just My Style Series, Year of the Tiger, Ship-Shape, The Gambler, The Chess Queen
What it means:  To win this Challenge, the required games must be played in order.  The second-listed game will not award any credit unless you have finished playing the first game for the indicated time. 

So, "John Deere" is the first game, "My Farm" is the second, "Magic Farm: Ultimate Flower" is the third, and so on.  Credit cannot be earned for "My Farm" until you have logged 120 minutes on "John Deere."  And you'll need 120 minutes on "My Farm" to earn credit while playing "Magic Farm: Ultimate Flower," etc.  Unlike other trophies, where games can be played in any order, or all at once, this type of Challenge requests you play in a specific progression.

This does not mean you have to play all 120 minutes in one sitting--you could play 30 minutes of "John Deere" this week and 30 minutes next week, and you would still have 60 minutes total credited.  It only means that until the bar is full for "John Deere," no amount of playtime will be counted toward "My Farm," and so on.