So here's the low down on "breech" and "breach":
Breech means the back of something. The breech of a gun. Most modern firearms are "breech loaded" (as opposed to muzzle loaded). A baby coming out bottom-first is a "breech baby." You wear "breeches" because they cover your ass.
Breach means a break or fissure. You breach your contract. The torpedo breached the hull of the battleship. To kiss the queen was a breach in protocol. And whales jumping into the air are "breaching" (perhaps because they breach the surface of the ocean?).
Oh, and the Shakespeare quote from Henry V: "Once more into the breach."
How to remember which is which. This is easy. "Breach" has the same five first letters a "break" which is one of its meaning. And "breech" has two e's so you'd say "eeee" if you saw someone's breech.
So don't breach good spelling rules and come out looking like a breech.