I'm also tied for first in Revolution and Quickening Finesse, and I have untied first place for Resilience Finesse (edit: FYI my current Resilience Finesse score of 36 is a bug, my real score is 50). I also have every achievement except for completing 100 daily challenges.
Finesse is the number of touches you use to complete the levels. The fewer the better. When you replay any level, it counts the touches you use in the top left corner, so you can see how you're doing. If beat the level when the counter hits 0, without getting into red territory, then you have perfected the level and a small green triangle appears for that level on the level selection screen.
Perfecting every level is a good start. But how do you get a really world class score? The secret is some levels can be completed with a better than perfect score. But how do you find them? It's a lot of work, but I'm going to help you out. Here is a list of all my better than perfect levels and the number of touches possible to save. This took a lot of work to create, which you won't have to do. Use my list and you can save time by not carefully analyzing levels where the "perfect" score really is the best possible. (But analyzing the levels is fun, so it's up to you!)
Denial VI +2
Anger IV +1
Bargaining III +1
Bargaining IV +1
Bargaining V +1
Bargaining VI +1
Hope I +1 (Thanks AWPrince)
Hope III +2
Hope IV +4 (Had +3, several people told me +4, thanks)
Hope V +1 (Thanks Adrian Ensan)
Acceptance IV +1
Acceptance VI +1
Acceptance VIII +1
Acceptance IX +1
If you get every level perfect and then match these scores for better than perfect results, you will achieve a total finesse score of 384, pass hundreds of thousands of other players and reach the very tip top of the leaderboard.
July 31, 2014 brought Duet version 2.0 with 48 new Epilogue levels with their own finesse leaderboard. I scored 311 right after release which was first place by a large lead. Want to see me learning the game for the first time? I've got videos with commentary:
Epilogue patch day part 1 video
Epilogue patch day part 2 video
(Two parts because Windows crashed.)
My current score is 260. I was the first player to get every level perfect, which I did in under 24 hours from release.
Here are the Epilogue Finesse tricks found so far:
Trust VI +1 (Thanks Keiran)
Control VI +1 (Thanks Keiran)
Initiative V +1 (Thanks Keiran. VERY HARD)
Identity VI +1 (Thanks Keiran. left-touch-death, spin through first arrow)
Intimacy VII + 1 (Thanks Adrian Ensan)
Intimacy VIII +2 (Thanks Keiran for the +2)
Intimacy IX +2
Integrity III +1 (2 spike tricks then very hard spin around block and end at glide through 5th spike angle. VERY HARD)
Integrity IV +3 (left-touch-death, see below)
Integrity V +2 (Thanks Keiran for the +2)
Integrity VI +1
Integrity VII +2 (Thanks Keiran for the +2)
Integrity XI +1 (perfect angle can go between last 4 squares)
Duet's Three Positionings: To do all the tricks you have to understand a bug in the game. When you die, you will start the level in a slightly different position depending on whether you were holding left, right, or nothing. When you first enter a level, you will begin with right-death positioning. The slight change in positioning changes which tricks are possible. The change is visible if you watch the animation very closely at the end of the rewind after a death. It's easier to see with a left-death. With a right-death, there is a tiny stutter that's barely visible.
Some levels require you intentionally die while holding the right direction before you can do all the finesse tricks. Note that you have to do this on every other life, because the effect only controls your next life.
The best level to test the death positioning physics on is Revolution 1. If you do a left-death, you can then do two right edge spinners with one touch on your next life. If you do a right-death, you can then do two left edge spinners with one touch on your next life.
This bug was very hard to find and understand, but is easy to use. Try to appreciate the work that went into it, lol. Although a specific death is only required on a couple levels, it makes a number of other levels a little bit easier. If you're having trouble with any level, try right and left touch deaths and see if either one helps. For example, I believe Integrity III might be easier with a right-touch death.
Videos: I also made some videos to show tricks:
Understanding II Perfect Finesse Video
Integrity VII Finesse Trick Video
Integrity VIII Finesse Trick Video
If you get everything perfect, you'll score 279 finesse. Add these tricks to reach 260 Epilogue Finesse.
And here's a general tip: for the two moving small dots, or the two spike pieces that move together or apart, you can go through infinitely many in a row in one touch, if they are all lined up at the same angle. If they are straight up-and-down vertical, you just have to place your top ball at around 1:30 or 10:30 on the clock and then don't move. This works even if you get both different types of small dots (the ones that are together or apart when you pass them).
The concept of how to get the right angle before these blocks, and then go through them without moving, is really important for getting good finesse on the early levels which introduce those types of blocks. It's also needed on more complicated levels. But just to get started and do early levels, you need to know this!
My endless score is currently 29,100 (in the top 25). Practice, practice, practice!
Secret Bonus Level: Did you know Duet has a secret level? It's called "Transcendence S", and it's like a cross between Transcendence and Quickening. It's hard, but tons of fun. To play Transcendence S, beat Transcendence III without dying. (If you die, you can exit out of the level and restart it.)
To further help your Duet leaderboard aspirations, I've also decided to share my scores and notes about the other finesse categories. This will help you understand what a good score on each level is, where you can improve, and the odds of getting really good level layouts on the randomized levels. All of the B-side levels are randomized except for Resilience III. The numbers in parentheses are the number of touches the level considers "perfect", and a +6 would mean I saved 6 touches better than "perfect".
revolution score: 14, untied first place
revolution 1 ( 7) +3 (cannot improve)
revolution 2 ( 7) +3 (cannot improve)
revolution 3 (13) +7 (cannot improve. note +7 requires estimated 1/359 odds layout)
The trick to Revolution is to do two spinners at a time with one touch. This requires both spinners to go the same direction. Think of direction as which thumb you press to spin around it. If both spinners use the same thumb, then they are the same direction, and you can do two of them with one spin. This is easiest when both spinners are in the middle. If one spinner is in the middle and one on the edge, it still works but the timing is more exact. If both spinners are on the edge, then it's impossible to do those two spinners together with one touch.
Edit: Getting above +0 on revolution 1 requires using a bug. See the information above about killing yourself while holding left or right.
quickening part 1 score: 3, first place
quickening 1 (7) +6 (cannot improve)
quickening 2 (7) +6 (cannot improve)
quickening 3 (7) +6 (cannot improve)
quickening part 2 score: 3, first place
quickening 4 (7) +6 (cannot improve)
quickening 5 (7) +6 (cannot improve)
quickening 6 (7) +6 (cannot improve)
Note: Estimated 1/50 chance for 1 touch quickening layouts
Edit: Adrian Ensan pointed out that you might be able to get a level with all middle blocks for some quickenings and get a 0 touch (+7) result.
I recommend playing through all the quickening levels in a row until you have the no death achievement, don't die very often, and get several one-touch levels completed. Doing it that way is fun and good practice. Then to finish things up at the end, you can play individual levels and reset the moment you're forced to use a second touch.
resilience score: 50
resilience 1 (25) +13 (good score, better is possible)
resilience 2 (35) +20 (good score, better is possible)
resilience 3 (25) +2 (This non-random level was formerly "Acceptance VI" in older versions of Duet, and was the hardest A-side level which blocked many players from finishing the game)
transcendence score: 14
transcendence 1 (12) +11 (cannot improve)
transcendence 2 (25) +21 (good score, better is possible)
transcendence 3 (50) +41 (good score, better is possible)
Do you know somewhere to save finesse that I missed? Do you have a better score than me in anything Duet related? Got any good strategies? Post in the comments below.