I've always envisioned an achievement based DK game that gave you more abilities as you slowly fulfilled achievements within the game. This game could either be played on a 'one time mode' -where once you run out of men the game is over and all the collected abilities are lost, or else on 'play though mode' where even after your game ends, all the achievements and abilities you've gained would stay.
Granted, this would be a tough concept to think through so as not to make some achievements too hard while also not making some abilities too good, but here is an example of what I'm thinking:
Jumpman can only move right. You are on the barrel screen. There are only 1000 bonus seconds on the timer!
You move all the way right and hit the wall, and all of a sudden a blinking box appears up at the top of the screen that says you have acquired an ability and to push P1.
You push P1 and a menu opens up that shows you a whole checklist of achievements, and so far you have only gotten one. Most achievements are simple, but they are only hard because of the abilities you will ultimately only have by the time you need to try to achieve them. The "Touch the right wall" achievement tells you that you can now move left. You see another achievement is to touch the left wall.
You push P1 and it starts you back at the beginning of the screen with 1000 still on the timer, but this time you can move left.
You touch the left wall, and the same menu up top flashes.
You press P1 to find out now you can jump. The achievement need to be able to climb up ladders (but not down) is to jump 5 barrels in a row.
You start the game again and achieve this.
Next you need to need to get to the 6th girder with only these abilities to earn 1000 more bonus time for this screen.
You do this.
Next you need to finish 1-1 with only these abilities to acquire the ability to climb down ladders.
You beat 1-1. On the rivet stage you realize that you can't grab hammers (it won't let you) nor can you remove rivets! However, there is full normal bonus time. You check the menu, and realize you need to leach 3000 points off of Kong amidst all the free roaming fireballs to earn the ability to use just the top hammer on this screen!
You go and achieve this. You still can't use the bottom hammer quite yet though.
Next, in order to be able to clear rivets, you need to get 5 fireball smashes with the top hammer.
You go and do this.
Etc. Etc. Etc.
Ultimately there would be some achievements incorporated into the game that would be tricky or quite hard. There is a wide range that people could come up with, and I can see some achievements being related to each other in very interesting ways such that you need to do a certain one before you can get others. Sometimes even specific screen is in incomplete and impassable until you fulfill some achievements (like imagine if platforms were missing on the elevator board or if 30 fireballs spawned right away on the pie factory!) At the start of the game more time would be spent more or less getting the game back to what we are all used to, by 'restoring' it through unlocking achievements. Later on, it game would have the more typical DK feel and the challenges would have more to do with surviving or getting points, while some of the harder ones would actually be a lot like some of the challenge ideas people have posted elsewhere on this forum.
Many of the rewards for achievements would solely have to do with affecting Jumpman's abilities, and sometimes only in rare situations. The trick would be too never make abilities so powerful that it absolutely ruins the natural feel of the game we all love. Also, you would want the game to still have the characteristic of getting harder the more you try to point press, so these abilities would have to basically increase the potential of what people can do to try to get points, without just giving the player an easy way to cop out of difficult stuff by exploiting a silly glitch or loophole in pressing strategy that makes it all too easy. The better abilities would probably have to be either temporary or conditional. Below are some I have thought up, but the sky's the limit:
-The ability to wield a hammer on ladders.
-The ability to jump with the hammer.
-The ability to sacrifice points in exchange for other temporary abilities or to change certain elements of the game (Maybe like freezing the fireballs for 1 second per 10k points, or 20k to turn hammers into super hammers which give 10x the points on smashes, 2k to stop the conveyors or springs for 1 second...etc).
-Make Pauline's items give temporary upgrades or affect the current screen temporarily.
-The ability to do super jumps upon landing the first time if you hold down the jump button during the entire first jump.
-The ability to go to 2x speed for 3 seconds by doing some sort of up-down-up-down motion while on the girder, but time clicks down 2x faster as well during this period while the rest of the gameplay is normal speed.
-The ability to do double jumps in the air or wall jumps by jumping and press the up direction at any point in the air.
-The ability to slide all the way up or down ladders super fast by pressing the jump button and an up or down direct while on ladders, however, all control is lost until the end of the ladder is reached
-The ability to jump onto ladders by the up or down direction while jumping past them in the air.
The ability to jump off of ladders by holding a left or right direction while on a ladder and pressing jump.
You get the gist of it. Needless to say, I've fantasized about a game like this for quite a while!