I'm also facing problems while trying to manually install this. I'm not sure if this is recent with PHP 8 beta3 or it happened before as well. I can't find any references to that in this issue.
First, I faced problems with incompatible method declarations in doctrine/reflection. I'm on the latest 1.2.1 release and see an error with methods getConstants and newInstance. I manually fixed both those instances (it was trivial) and it moved ahead.
After I entered the database details, I got an error with PDO and I have not tried working around it yet (because the method definition is in the interface as well). This is the error I see:
Fatal error: Declaration of Drupal\Core\Database\Statement::fetchAll($mode = null, $column_index = null, $constructor_arguments = null) must be compatible with PDOStatement::fetchAll(int $fetch_style = PDO::FETCH_BOTH, mixed ...$fetch_args) in /var/www/html/web/core/lib/Drupal/Core/Database/Statement.php on line 169
Now, this class extends the \PDOStatement and also implements \Drupal\Core\Database\StatementInterface. I'll have to change the method signature in both the places which seems like a big change. The funny thing is I couldn't find any information about this online. I'm not sure if I'm just missing something here. I did verify I am running PHP 8.0.0beta3 with build date on Sep 10 2020 13:18:12.