Substitute a K for the CH in “breach” to remind you that the word has to do with breakage: you can breach (break through) a dam or breach (violate the terms of) a contract. As a noun, a breach is something broken off or open, as in a breach in a military line during combat.
“Breech” however, refers to rear ends, as in “breeches” (slang spelling “britches” ). Thus “breech cloth,” “breech birth,” or “breech-loading gun.”
“Once more unto the breach, dear friends,” means “let’s charge into the gap in the enemy’s defenses,” not “let’s reach into our pants again.”