This is indeed a challenging kakuro puzzle!

Here is how to solve it:

Using basic techniques (sums/combinations), we could reach the following state:

Here Red+Yellow cells=30, and the Red cells cannot be 4 or 5 otherwise we'll have a naked subset of {1245}=12 forcing the remaining 2 cells to sum to 18, impossible...

Since Blue+Green cells must sum to 25-2-7-3=13, the Blue cell cannot be 9 as the Green cells sum to at least 1+4=5, so it must be 8...

Here it gets quite tricky... We can use the "difference" technique (a popular technique for killers) to work it out:

Across (Violet+Orange):

21+28+24+22=95

Down (Violet):

24+16+30+13=83

Orange=95-83=12=6+6

(Alternatively, you can work on the right hand side of the grid, so the 2 cells above the Orange cells sums to:

(8+15+13+23)-(14+18+15)=59-47=12=3+9)

Solution:

I think we probably could apply some Unique Rectangles on the bottom left area to work around the "difference" technique, but I'm not familiar in that department...