I'll keep this relatively simple for now (no need to write
everything I could say). If you have more in-depth questions, just ask, and I'll go into more detail for you.
Picture 1: The goal here is to get to the bottom right corner. Getting to this corner allows you to steer barrels off the screen. You may have to jump a barrel to get to this corner, but be mindful that it's almost always the
2nd barrel that you need to be worried about. It'll take some practice, but you'll need to learn how to coordinate jumping the first barrel with either a standing or front jump as to not put yourself into a unsurvivable situation with the next barrel. Many times, simply getting ahead of the first barrel and placing yourself just to the right of it as it hits the end of the 2nd girder will send it off the screen. Once in the 'safe' zone, keep in the back of your mind that barrels can still land directly above you on the end of the 3rd girder and head for you!
Picture 2: Simply wait in the safe zone until DK throws a barrel straight down rather than at you, then go for the ladder and climb up. Try to stay as little to the right of the barrels you are steering as you can, that way you are just that little bit closer to the ladder when your opportunity comes.
Picture 3: There are many ways you can get to the 3rd girder, but this is just the one I prefer. I don't like using the short ladder, cuz in the hack DK can throw some mean 'bomb-like' and also very zig-zagy type wild barrels on the left side of the screen. I'd rather not have to traverse that area of the screen. For this method, simply steer barrels above you as they are hitting the
4th girder. Immediately attempt to climb the ladder afterwards. Many times the next barrel can cause you to have to retreat do to it's randomness. If it does, simply retreat and patiently try again. If the fireball climbs up, you may need to grab the hammer and smash it and simply delay your climbing till later. You'll need to become a master at avoiding successive wild barrels while on one girder in order to feel comfortable not rushing, but doing this allows you the best chance of survival.
Picture 4: This is much like picture 3, but in with an extra part. However, realize that wild barrels are able to go right quicker than they can go left, so incorporate this into the situations where you may have to retreat. The biggest struggle in this section is being able to make the trip to the area highlighted to the right of the middle ladder (again, I don't take the short ladder, as in this case it is just
way too difficult to have to get past the sidewinders that go all the way right -and
twice, at that! You'll have to incorporate some jumping over wild barrels that are in-the-air-and-coming-back-at-you to allow yourself to time to make it to this rightmost area. However, this is necessary, since it affords you the best chance to climb the ladder with the most control over the wild barrels (safety, that is). Once you get to the right area, do the same thing you did before in picture 3, but realize that you have less time to react to the second barrel in this area than you did before, since you are up closer to DK. Sometimes the 2nd barrel will cause you to even retreat back to the left area, and you may have to do the entire process over again. I find this to be the hardest part of the entire screen.
Pictures 5 and 6: Once you climb the ladder, simply steer the barrels to the right before making your way left. Most the time the barrels will go way over your head to the right, but every so often the barrel will bounce and do what I call a 'knuckleball' and will slowly head right for you. In this situation you need to jump to the right and then reposition yourself. This takes fast reaction, but it only happens a very small minority of the time. Once you start running left, you may need to jump to keep the next barrel from hitting you from behind in the heels. Position yourself just to the right of the left ladder, in the path of where 'bombs' would normally be thrown. For the most part, this is a safe zone, but pay attention, cuz every so often some barrels can still hit you from the right. If you move a little bit too far to the left, the barrels will start bouncing to the left, and you don't want that.
Pictures 7 and 7.5: These pictures highlight the
two main types of wild barrels DK will throw when you try to climb the left ladder (p.s. I'll probably die in both the pictures, but that was cuz I needed to take a screenshot at the same time, so just understand my placement is a little off in both). Wait in the 'safe' zone until the moment a wild barrel bounces out of DK's hands and to the right, then quickly attempt to climb the ladder. For picture 7, DK has thrown a barrel that pretty much comes right at Jumpman, in this situation you
must retreat! Retreat back to the safe zone and try again. For picture 7.5 DK has thrown a wide-left wild barrel (this is the picture I am really out of position on). In this case, you can continue climbing, but you must immediately jump to the right once you get to the top of the ladder (if the barrel is still gonna hit the 5th girder -sometimes they go so far left initially that you don't have to worry about it) to keep the barrel from nipping you in the toes. Place yourself just to the right of where 'bombs would come out; this is almost 100% a safe spot (there may be a few pixels width which actually are 100% safe).
Pictures 8 and 8.5: Wait in the top 'safe' zone until DK throws a barrel as far right as he can and then run and follow it as closely as you can. Some barrels bounce more to the right more than others, so you'll need to train your eye to see which are which as closely as you can to their initial bounce (kinda like level 4+ springs!). Make sure to jump if you need to to avoid getting hit from behind by the following barrel. Picture 8.5 is merely demonstrating how far the farthest barrel can basically reach, and why you may need to jump.
I hope this helps! Cheers!
Again, feel free to ask me questions!