In one of the subway projects in Hamburg, a cost of 1.1 billion EUR per kilometre was reached.
But that project was building a subway including station directly below a riverbed.
Well, that's some adverse conditions - a silt riverbed behaves quite like water, so you're actually building a submerged part of the city. Look at London's early tunnels and their cost overruns (and the maintenance due to leaks).
The closest thing is the Regional Connector project, which will be 1.9 miles of light rail and has a budget of $1.8B. But that's the entire project budget. Tunneling costs are only part of it; it's hard to find a finely grained budget, but total construction (including four new underground stations) is budgeted at $1.2B here [1], which is still "just" $600M/mile.
[1]: https://mtadash.mlmprojectservices.com/projects/5773#/cost