Incredibly high tactics trainer ratings

I can think of a few possibilities.

--There is a limited stock of very hard problems.  It may be possible to memorize most or all of them.

--You might be able to exploit the software, for example by manipulating disconnects so that you are never scored as wrong for a problem you can't solve.  (This would pair nicely with the previous one.) 

--There might be some way to get an engine involved.

I notice that the top players on Puzzle Rush are almost invariably titled players.  It may be harder to manipulate Puzzle Rush as it doesn't serve very hard problems (there are too many easy problems to memorize them all) and disconnecting ends your game.

I think it's best to think of Tactics Trainer ratings as your competition with yourself--can you beat your previous score?--and not with other players.  I also find, personally, that it's better to try to get every puzzle right--I often pledge to stop and do a house chore if I get one wrong--rather than trying to do them quickly, which can teach you to rely on lucky guesses too much.