Well I just finally beat the game this morning on single player Double Dragon difficulty, so here's a few more tips:
Spin Kick is really useful in many situations for its invincibility, knockback, and damage, so I'd recommend putting a lot of mythril/money into upgrading it. Very good for beating bosses like Skullmageddon and the mandroid, especially if you dodge an attack to get gleam first, then use it on them. It's also good against Abobos as the invincibility will protect you when they
swat at you with their powerful attacks.
Lightning can also be really OP when you get it fully upgraded and combine it with a tape like Power Gambit or Successive Strikes. You can kill most of the early enemies on Normal difficulty with just one blast with those tape combinations maxed. It is also REALLY handy in dispatching those annoying-as-hell flying Roxy girls, the Rocketeer-esque jetpack ladies. I think with maxed Power Gambit and Lightning it takes around 5-6 blasts to kill them on DD difficulty, but it's a good trade off considering how much trouble it will save you, and the lightning can deal with a bunch of them and other enemies besides all at once.
Healing Touch is great when you get it maxed because it heals a good chunk of health, especially if you have a maxed Power Gambit. In DD mode, keeping your health up becomes critically important because the enemies can kill you in just a few hits on the later missions and you may need to use this to save your bacon.
Plus, you can not only use it against enemies or your bro (in bro-op mode) but on breakable objects as well! Yup, it makes no sense, but you can actually use it on a vase, trash can, statue, lamppost, or other breakable things and get health back! Very handy if you're near death and the only breakable thing around isn't one that has a health-restoring soda.
If you're really struggling, go and get FuzzyFace in mission 6 by ducking 7 times between the two gravestones. He can be annoying to listen to after awhile, but the sodas and batteries he drops roughly every minute or so can save your ass in a pinch. If you get him, he will show up to help you in every mission you play after that, until you quit the game and resume play on your file. Then you'll have to go back to level 6 and get him again if you want his help.
As for missions themselves, the hardest ones for me were mission 6 and mission 9. For mission 6, just make sure you don't get killed by the helicopter blades in the first half of the mission. If you survive that battle, it's not that much farther to FuzzyFace if you need him. In the section immediately after that with the arrows raining down, dispatch all the enemies, and then
MAKE SURE YOU ALWAYS TAKE THE UPPER PATH TO GET THE FREE MONEY AND TWO EXTRA LIVES! Run and time your jumps to avoid the arrows, and use your stronger jump kick to get the extra distance needed to clear the long gaps. When you get to the tank battle, concentrate on destroying all the gun turrets and smokestacks (preferably with Spin Kick) in the first round because you don't need anything extra coming at you in the later rounds. Make your way up to the platforms on the top-left, then cross over the top of the tank and take out those two big pipes that shoot out the rocks. Finally, jump to the platform on the far top-right of the screen where there is a line of explosive barrels. Now pick up the closest one, turn around and throw the barrel at the tank's big, red weak point. Bang! Round 1 over! Repeat this process once more for each round and
YOU CAN DESTROY THE TANK IN ONLY 3 HITS! 
Mission 9 is also a huge pain in the ass because of the total length, the way it starts out and the strength of the undead enemies later on, especially in DD mode. It's just plain hard, no matter what tapes you're using, and you may need to do a lot of tape switching to get through it. In the beginning ride on the plant platform, you've really got to be on your toes to keep up with the enemies. Try to knock them off and throw them off the platform ASAP. When the Roxies show up, use Lightning to blast those bitches out of the air and send them packing. If you make it to the lone Abobo at the end, one well placed Spin Kick right in the middle of him should knock him off the platform. In the remainder of the mission, make use of
the big, fleshy bone clubs as much as possible because every hit restores health! Also use Absorb and Healing Touch when necessary to keep that health up. Remember that the skeleton enemies cannot be stunned, so you must plan accordingly for their near-constant attacks. When you get to the part with the key,
DON'T PICK IT UP RIGHT AWAY. Go down the ladder and clear out that next area of enemies, then you can go back and get the key. Put on your Spin Kick for the tapeworm in the next section because the treasure chest is just after the tapeworm, but you'll have to keep holding the key, so you won't be able to punch without throwing it away. A couple Spin Kicks will let you get in several hits though anwyay.
As for beating Skullmageddon and Giga Skullmageddon in mission 10, make sure to find the secret shop (just follow the yellow arrow in the falling platform section, same as in mission 8 ), buy extra lives if you need them, and plunder the secret area after going through the Portal of Love (extreme bottom-left corner of screen, down hidden ladder) for two treasure chests and 3 extra lives!
Hope this helps you guys!
The shop guys and the tapesmith are a hoot too. Play control feels good and just like how a modern DD should feel. Marian looks sexier than ever, and the soundtrack is SO RADICALLY AWESOME DUDES!!! 
