Use filldraw
and the path must be a closed one, so you need to add ..cycle
and provide a color as rgb(254,248,128)
. Note also that the varwidth
option which suppresses the extra added width is used to have a symmetric standalone pdf.
\documentclass[border=5pt,varwidth]{standalone}
\usepackage{asymptote}
\begin{document}
\begin{asy}
size(0,150);
defaultpen(linewidth(1pt));
filldraw((0,0){up}..{right}(3,3){down}..{left}(1,1){right}..{up}(2,2){left}..{down}(0,0)..cycle,rgb(254,248,128));
filldraw((0,0){up}..{right}(2,2){left}..{down}(1,1){right}..{up}(3,3){down}..{left}(0,0)..cycle,rgb(128,127,255));
\end{asy}
\end{document}

Update
To add a grid, use add(grid(x,y));
after including import geometry;
. You can change linetype, color, width, etc. of the grid. Here is an example:
\begin{asy}
import geometry;
size(0,150);
defaultpen(linewidth(1pt));
add(grid(3,3,gray+.5bp));
filldraw((0,0){up}..{right}(3,3){down}..{left}(1,1){right}..{up}(2,2){left}..{down}(0,0)..cycle,rgb(254,248,128)+opacity(.8));
filldraw((0,0){up}..{right}(2,2){left}..{down}(1,1){right}..{up}(3,3){down}..{left}(0,0)..cycle,rgb(128,127,255)+opacity(.8));
\end{asy}
