Earlier quoted context omitted.
Asking the database administrator in you, what's the most efficient way to do it? Queue and push updates every 10 minutes?
If I had to use the database, I'd probably aggressively shard the data so that it's spread across multiple databases/tables. That way the load of counter updates could be spread across machines. I'd probably also store the counters in a separate table from the rest of the levels, for the same reason, but also to ensure that the rest of the information about a level isn't locked during every increment. Of course, this…
Also ideal is to have the client not update the number of deaths on each attempt but only either on completion of the level or at a timed interval. No need for that date to be real-time, so it can be aggregated.