To achieve the first level for your matrix badge, you need to find over 20 distinct combinations of the 5x5 Difficulty/Terrain rating. The combinations required for each level increases in growing increments, so it gets harder to get the last levels. The most combinations possible is 81 (9x9).
To achieve the first level for the shutterbug badge, you must upload 50 pictures to any geocache logs. You can upload more than one picture per log, although it is not necessary. The levels also increase in growing increments, so it takes longer to achieve the last levels for this badge too.
I hope this helps you.