"At a sacrifice" is a phrase often used to describe a situation where one must give up something valuable in order to achieve something else. There are many synonyms that can be used to convey a similar meaning, such as "at a cost," "at a loss," or "at a price." Other options include "compromising," "cutting corners," or "making concessions." Each of these phrases suggests that there is a trade-off or difficult decision to be made in order to achieve a desired outcome. Ultimately, the choice of synonym will depend on the specific context and the level of sacrifice that is being made.