UPDATE: as of mid-july 2014 this achievement is 'fixed' by BB - now you can use Soldiers but no cav any more
For the achievment "horses can't swim":
As you see it says you can still use Cavalry - but the normal Soldier isn't mentioned. This is a very fortunate error from BB --> you can complete the achievement with bringing horses, but do not bring a single Soldier!
As long BB this hasn't adjust it works. I tried it with cavalry & it worked flawless.
(and leave the Master of Martial Arts general at home as well - he count as a type of unit)
With one of the next few updates (mid june 2014?) it will be adjusted:
Horses Can't Swim
- BB dev diary detail added