Unwanted vertical separation between tcolorboxes

You need to cancel the natural \lineskip:

\documentclass[12pt,paper=a4]{scrartcl}

\usepackage[lmargin=0.9cm,rmargin=0.9cm,tmargin=26.5mm,bmargin=26.5mm,showframe=true,a4paper]{geometry}
\usepackage{tcolorbox}
\usepackage{lmodern}


\begin{document}
\setlength{\parindent}{0pt}%
\setlength{\parskip}{0pt}%
\pagestyle{empty}%

\fontsize{80}{96}\selectfont 
\offinterlineskip
\tcbset{height=61mm,nobeforeafter,top=2cm}
\begin{tcolorbox}%
\textbf{\LaTeX}%
\end{tcolorbox}
\begin{tcolorbox}%
\textbf{is}%
\end{tcolorbox}
\begin{tcolorbox}%
\textbf{very}%
\end{tcolorbox}
\begin{tcolorbox}%
\textbf{sophisticated}%
\end{tcolorbox}

\end{document}

In the above example, \offinterlineskip will have effect from the point where it was issued on. To have suppress the \lineskip in a more controlled way, one could use the after key in with

after=\par\nointerlineskip

as Thomas F. Sturm suggested in his comment.

The spacing is due to \lineskip; the usual setting of \parskip is to have zero natural width, so it can add vertical space only when \flushbottom is set, because it has a stretch component of 1pt. In this case, you should set it to zero and also set \lineskip to zero, but in a group to avoid the setting going on forever.

\documentclass[12pt,paper=a4]{scrartcl}

\usepackage[lmargin=0.9cm,rmargin=0.9cm,tmargin=26.5mm,bmargin=26.5mm,showframe=true,a4paper]{geometry}
\usepackage{tcolorbox}
\usepackage{lmodern}


\begin{document}

\begingroup
\setlength{\parindent}{0pt}
\setlength{\parskip}{0pt}
\setlength{\lineskip}{0pt}

\fontsize{80}{96}\selectfont 
\tcbset{height=61mm,nobeforeafter,top=2cm}
\begin{tcolorbox}
\textbf{\LaTeX}
\end{tcolorbox}
\begin{tcolorbox}
\textbf{is}
\end{tcolorbox}
\begin{tcolorbox}
\textbf{very}
\end{tcolorbox}
\begin{tcolorbox}
\textbf{sophisticated}
\end{tcolorbox}

\endgroup % the empty line is needed

\end{document}

Why is \lineskip intervening? Because each line has height plus depth larger than \baselineskip, so the difference between “depth of the line above plus height of the line below” and \baselineskip is larger than \lineskiplimit (usually 0pt), hence TeX inserts \lineskip glue, thinking that the lines are too near to each other.

A different solution, from a comment by Thomas F. Sturm, is adding after=\par\nointerlineskip to the options to tcolorbox:

\tcbset{height=61mm,top=2cm,after=\par\nointerlineskip,before={}}