The phrase "achieve stalemate" refers to a situation in which opposing forces or parties are unable to gain an advantage over each other, resulting in a deadlock. Synonyms for "achieve stalemate" include "reach an impasse," "hit a deadlock," and "come to a standstill." Other similar terms can include "lock horns," "reach a draw," and "standoff." These phrases are often used to describe situations where negotiation or compromise is needed to break the deadlock and move forward. In political or business contexts, achieving a stalemate may mean that both sides need to reassess their positions and come up with new strategies to achieve their objectives.