Hi, You posted this some time ago, so I am surprised it hasn't been answered yet.
This is a crab of the family Dromiidae - known as the sponge crabs. Some nice photos, thanks for posting.
The sponge crabs are usually small to medium sized crabs, but the one you have here seems to be reasonably big. I can't offer anything definate on the exact species, especially as I am not familiar with crabs of the Philippines, but it is certainly one of the sponge crabs, and possibly the species Dromia dormia, but I am open to correction there!
The name sponge crab comes about from this crabs usual, yet unusual habit of removing a sea-sponge from a rock and manouvering it to be carried on top of the crabs carapace. Look at the photographs of its much reduced back legs - these legs are used to hold the sponge in place and would prove next to useless for walking. In time the sponge will grow over the carapace of the crab, and the crab will use this natural cover as a form of camouflage.
Most of the surface of these crabs are covered in a fine but stiff hair, probably to aid further in the camourflage theme.