Here is a full walkthrough for this masterpiece!
1. Step:
L inside steelbox
R (jump U) to get coin.
Jump L to get other coin.
D and slide R inside barrel.
R pushing barrel L to dancing Z-bot.
DU to remove breaktile.
L over ice and through TP on white button.
2.
L through TP, pushing steelbox R.
Follow, jump UL inside barrel.
D pushing barrel U in water.
U on barrel.
L to get coin.
UL over ice through TP.
L through TP
R jumping UR out of island.
3.
Go to Marquis' area, where the chomper and the 2 steelboxes are.
Push box up into left TP and (after a few milliseconds) enter the middle TP. When timed correctly, Loof will merge with the box on the aqua button. Take coin, step down and push box on black TP left. You will teleport to the separate island with 3 tiles below. Don't take the coin. Instead, go left into the black TP and lure the chomper to the left side. TP down quickly to avoid chomper and appear on the right side. Push box up into right TP and enter the middle TP. Keep pressing the down arrow key until you merge with the box on the island below. Finally step right to take coin on break-tile and exit left.
4.
Lure the chomper to explode the barrel, with the boulder at the right side.
Get right one of two coins, above 2 icecurves.
Push right one of new generated boulders D, to explode barrel bottom-right
Get coin on breaktile, right-above boulder generator.
Push other boulder left, to destroy goobie. (it goes on pink button.)
5.
Push upper one of three woodboxes at the right side: R, 4D.
Push it 4L, U (walking twice around the lake.)
Push lower one of 2 remaining boxes, to where coin was above 2 icecurves, mentioned above.
Push it D, and immediately step L, getting other coin.
Push it 2U.
6.
Go through pink gate and push goobie U through hidden white TP.
Follow and get coin 2 left of lower white TP
Go R through TP and R again, jumping UL.
Walk all the way U and jump U to above island.
Walk R over breaktile
7.
Push box R, 3U, L to put flame out on hidden tramp.
Third of three boxes (still untouched so far) the same way, over the icecurves, and 2U.
Jump (using hidden tramp, mentioned above) LD
Push box the same way, jumping on middle goob.
8.
Go again through pink gate and hidden white TP.
R through TP, again R and jump UR.
Push box the same way as the other two, destroying other box between goobies.
Follow.
9. Push:
Right goob 2R over tramp.
Upper goob U, 3R, 2D over tramp on coin.
Left goob L, 2U, 5R, 2D over tramp on coin.
Let remaining 2 goobs jump D on right coin, using right tramp.
Get coins.
10.
Go to the bottom of the level, Jump L over tramp and blue gate. (Muzokoban!!)
Push box in the middle: 1R
rightmost bottom box: 1D, 1R
top-left box: 1D
top box: 2R
11.
right (top) box: 2D
middle box: 1L
left (top) box: 1U, 1R
middle box: 2L, 1U
12.
right (top) box: 1L, 1U, 2L
bottom box: 1L, 1U
bottom-left box: 1D
left (top) box: 1U, 4D
13.
bottom-left box: 4R
box above Loof: 2U
box 2 left of it: 1L
box 2 right of Loof: 2L
14.
At this moment, all woodboxes should be in an open gate, except for the bottom-right box, which is 1 tile right of an open gate.
Now, stand on the breaktile, activate the green timer, and in one very fast movement, push that last box 1L.....
15.
Get last coin, step L, R, and exit.