On the weekly NiconicoTV web show Yamamoto Producer showcased one of the new updates in the works for P&D, which is currently scheduled to possibly be implemented in September.
The details are still a little unclear, but it seems that monsters will get some sort of boost/awoken skill additions that provide incremental benefits and bonuses in dungeons. The examples given during the show were for Odin, Tyrannos and Yomi. From the monster detail screen you can see where there are a few boxes on the right side of the screen, and when you press on these you can access these awoken skills.
There will also be a little mark that shows on the monster box and lineup screens in the top right of the monster icon to indicate there are awoken skills.
For Yomi it was shown one skill where enhanced (boosted) dark drops would fall. Another one was shown where the time to move the drops/orbs would be extended (commented that this would help with Ra, etc.)
For Tyrannos it was shown a skill where attack is increased by 50 and one where HP is increased by 100.
For Odin it was shown one skill where the turn cooldown was boosted by 1. The other shown was one where there would be resistance to being bound by the enemy monster.
You can access the full Appbank story on this here.