Okay, I got the game and finally played a good part of it by switching to easy (had to try forever to even get past the first level on normal, totally imbalanced difficulty). In some ways it's really weak. E.g. the difficulty balance is really bad, the first 1.5 stages seem to be among the hardest parts of the game, especially with the first having hard to see enemies (those prone guys are almost invisible if you don't slow down and look for them) and lots of enemies taking a lot of shots to down (in the previous games they'd all die after one shot, at least in the early levels). The balance is basically set up so starting on Normal difficulty is impossible and you HAVE to use Easy to get anywhere and get enough time to learn how to play. Easy mode is really stupid as well, instead of reducing the number of enemies and bullets it seems like all they did was give you an obscene amount of extra lifes and buffed weapons (except for the standard peashooter which still takes forever to kill anything, feeling more like Metal Slug than Contra).
I think the only other Contra that gave me as much trouble on the first level already was Hard Corps. On Super Contra 3, Super C and Contra (arcade) I could get to the second or third level fairly easily.