I used to remember this game on the NES. It was great. One of the first games I got. Anyway, here's the scoop!
Quote Originally Posted by gonintendo
Darmstadt, April 12th 2007 - 10TACLE STUDIOS and 10TACLE STUDIOS MOBILE along with First Star Software, Inc. are proud to present the first graphics of cult gaming figure Rockford™ of Boulder Dash® fame. In Boulder Dash®- Rocks!™, the latest sequel to the 80s cult classic, our familiar well-loved hero appears with a whole new look. Both the logo and characters, as well as the in-game graphics, are designed to appeal to long-standing fans as well as target groups new to Boulder Dash, thus introducing a whole new Boulder Dash look.

The DS™ and PSP™ versions each offer at least one play mode custom-designed for, and unique to each platform. Boulder Dash-Rocks! is due for release on both platforms in the fourth quarter of 2007.

This challenging, arcade-puzzle game made its debut in the early 80s and continues to fascinate its enormous fan base decades later. Today the game is acknowledged as one of the classic cult games in computer gaming history. Now Boulder Dash® will appear with a hot new look sure to take the Nintendo DS™ and the Sony PSP™ platforms by storm. The hit game’s main objective and game physics remains unchanged: the player has to collect a certain number of diamonds while avoiding falling objects, traps and besting enemies in order to open and discover the exit, before time runs out. Of course there are a number of helpful tools made available to players such as bombs or laser guns which can be loaded with different types of ammunition. These lasers provide the player with different temporary powers, such as the ability to freeze enemies, destroy boulders and even pull diamonds and other distant objects towards the player.

In addition to the classic single-player mode, presented in several different worlds, Boulder Dash- Rocks! offers a multi-player mode as well as three additional game modes for a total of five play modes for each version. There are two new game modes, never before available in the Boulder Dash series, one of which has been custom designed for each of the two different platforms.
Source: http://gonintendo.com/?p=16068

Though not sure of the artistic style: