The same tactics that usually work against horse archers: heavy infantry with spears and shields or heavy armour up front, archers or crossbowmen behind or mixed in with the infantry and cavalry as a tactical reserve. The infantry formed a screen to protect the cavalry and the missile troops caused casualties among the attacking horsemen. The cavalry could then attack when a situation presented itself where the enemy cavalry was engaged or unable to quickly retreat.

This is how Richard the Lionheart fought in the Third Crusade, but variants on this formation and style of warfare can be found in use and in theory in history before and after this crusade.

As to breastplates, single piece breastplates couldn't be made at that time due to the small size of the blooms. You lose a lot of metal in the process of making a breastplate, about 3/4 of the original bloom weight, so blooms would need to be around 10kg in order for a single piece breastplate to be made. This didn't happen until well into the 14th century.

You could, in theory, make a breastplate by welding or riveting two halves of the plate together, and there is some evidence that Richard wore a riveted breastplate under his mail during tournaments later in his life, which is one of the earliest references to a breastplate in the middle ages. However, the breastplate seems to have been a novelty or a piece of tournament armour, rather than something that evolved as a defence against arrows.

In any case, the armour of the time was sufficient for dealing with the arrows of horse archers in this period, as Bahā' ad-Dīn attests:

"I saw some Frank foot soldiers with ten arrows sticking in them and still they advanced"

The mail and felt armour worn by the crusader infantry was sufficient to prevent any serious wounds by the Saracen arrows.