My first theory is that you somehow got a null value as a $profile.
In the file upgrade_2-0.sql, ~line 1776, change:
// Update the board tables.
foreach ($board_updates as $profile => $boards)
{
if (empty($boards))
continue;
$boards = implode(',', $boards);
To:
// Update the board tables.
foreach ($board_updates as $profile => $boards)
{
if (empty($boards) || empty($profile))
continue;
$boards = implode(',', $boards);
& let us know if this works!
*** Note php 7.2 is not officially supported at this time for 2.0.x. If you can go back to 7.1 you should do so. ***