First, shell is not python. Spaces around equal signs don't work:
DELETE = ($($MEGACOPY --dryrun --reload --download --local $LOCALDIR --remote $REMOTEDIR | sed 's|F '$LOCALDIR'|'$REMOTEDIR'|g'))
When the shell sees the above, it interprets DELETE as a program name and = as its first argument. The error that you see is because the shell was unable to parse the second argument.
Replace the above with:
DELETE=($("$MEGACOPY" --dryrun --reload --download --local "$LOCALDIR" --remote "$REMOTEDIR" | sed 's|F '"$LOCALDIR"'|'"$REMOTEDIR"'|g'))
Second, regarding the for loop, DELETE is an array and arrays have special syntax:
for i in "${DELETE[@]}"; do
"$MEGARM" "$i"
done
Notes:
Unless you want word splitting and pathname expansion, all shell variables should be inside double-quotes.
It is best practices to use lower or mixed case for variable names. The system uses all upper case variables for its name and you don't want to accidentally overwrite one of them.
for i in "$DELETE"; do. Notice the double quotes around$DELETE