Some player named mikhail--Botvinnik at 3700, but I highly doubt this is legit. Caruana's account has a score of slightly north of 3100 and there are about 10 people in between the former and latter accounts.
Highest Tactics Trainer Score?
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Not only was Caruana over 3000 but he had about an 85% pass rate too which is stupidly high.
In other words he easily topped out the system... the tactics were too easy for him 
So yeah, no one very much above 3000 is legitimate... especially if they have a very high pass rate. Well, they could be a GM.
Let's make it happen!
Let's make it happen!
Who has the highest tactics trainer score on chess.com?