Overall

I think you are very close to concluding a real MVP. The main issue with your program is what was expected at this point: having several entities that depended on each other, how to best pass references between these entities? You don't need to always instantiate objects inside other objects, you can instantiate objects in a separate class and then pass references, as needed, using setter methods or the constructor. If you tackle the issue with loading the images and the mouse, your program is basically working, because the logic for comparing cards and the timer is working. Tackling the issues mentioned above will make for a much better program. Also, don't forget to improve how the game starts (menu with instructions, for instance) and how it ends. A better game yet would include points and increasing difficulty somehow. If you decide to add different types of cards, consider if Interfaces and/or inheritance can help you.

• check for unused methods and variables
• you can improve how you use access modifiers
  • check when a method can be private
  • what is protected used for?
  • do you need package access properties?

Main.java

• nice and clean

Game.java

• what is the purpose of your start method?
• why not extract here some of the logic of setting up the necessary objects for the game?

Board.java

• nice, clean class, with clear responsibilities (create the board and the cards, determine matches and victories - because Board holds a reference to all the cards)

ArrayList v. array

• kudos for experimenting with a collection from the Java Framework to store your cards
• nevertheless, good old arrays are still valid
  • check if your game can benefit from how easy it is to access elements in an array (or nested array, in this case)

initBoard

• it's interesting how, in this method, each card's id is determined and shuffled
• on the other hand, you are using three for-loops in this method
  • check if you can create the cards, assign id's and shuffle them in one nested for

Card.java

• consider eliminating unused properties, methods and references
• when creating a card, you pass a size property on the constructor, that is never used
• why are you passing a reference to Board in the constructor of card?
• does Card need reference to a MyMouse?
• also, how many MyMouse objects are being created when you run the game?
• where is backImage initialized?
• beware of how you are initializing the Picture (resource's paths) - the problem loading the pictures arises from here
• otherwise, Card is a well design class - it clearly encapsulates the logic regarding each individual card (related to appearence, limits and comparing coordenates with the mouse, although contains is not the greatest method name!)

MyMouse.java

• so, everytime a Card is created, a MyMouse object is created and you pass it the reference to the Card that created it
• basically, this is one of the challenges of this exercise, which relationships to establish between objects (which object needs which reference to other object)
• consider, in a real world scenario, how many boards and how many mouses you would need
• if the Board holds a reference to all the Cards, maybe MyMouse only needs a reference to Board
• as I believe you already know, simplegfx is adding 37 px to the method getY of MouseEvent; if you take that in consideration, the mouse will select the card when clicked