Based on Nested enumerate (enumitem) interferes with suppressing vertical space after theorem heads. I use the following code. After a while, I ran into a weird behavior: As you can see, the sub-lists under 2. are not (vertically) aligned correctly. In 3., it is fine, though...
\documentclass{scrartcl}
\usepackage[american]{babel}
\usepackage{amsmath}
\usepackage{amsthm}
\usepackage{etoolbox}
\usepackage{enumitem}
% list settings
\setlist{% general list settings (enumitem's itemize, enumerate, and description)
align=left,
labelsep=*,
leftmargin=*,
topsep=1mm,% space before enumerate
itemsep=0mm% space between enumerate items
}
% theorems
\newif\ifstarttheorem
\newtheoremstyle{myexstyle}
{1em}% space above
{0.5em}% space below
{}% body font
{}% indent amount
{\sffamily\bfseries\global\starttheoremtrue}% head font
{}% punctuation after head
{\newline}% space after head
{\thmname{#1}\ \thmnumber{#2}\ \thmnote{\normalfont #3}}% head spec
\theoremstyle{myexstyle}% activate style
\newtheorem{exercise}{Exercise}
% vertical spacing when newtheorems start with an environment
\makeatletter
\preto\enumerate{%
\if@inlabel
\ifstarttheorem
\mbox{}\par\nobreak\vskip\glueexpr-\parskip-\baselineskip+0.3em\relax\hrule\@height\z@
\global\starttheoremfalse%
\fi%
\fi%
\def\tempa{proof}%
\ifx\tempa\mycurrenvir
\ifstarttheorem
\mbox{}\par\nobreak\vskip\glueexpr-\parskip-\baselineskip+0.3em\relax\hrule\@height\z@
\global\starttheoremfalse%
\fi%
\fi%
}
\preto\endenumerate{\global\starttheoremfalse}
\makeatother
\begin{document}
\begin{exercise}
\begin{align*}
f(x)=x^2.
\end{align*}
\begin{enumerate}
\item Show that ...
\begin{align*}
f(x)=\dots
\end{align*}
\item \begin{enumerate}
\item Foo...
\item Bar...
\end{enumerate}
\item \begin{enumerate}
\item Foo...
\item Bar...
\end{enumerate}
\end{enumerate}
\end{exercise}
\end{document}
