1 break a record

Shi Zhiyong of China has broken his own world record to win gold in the men's 73kg weightlifting event at the Olympic Games Tokyo 2020.

2020年东京奥运会男子73公斤级举重项目，中国选手石志勇打破自己的世界纪录夺得金牌。

2 set a record

They want to set a record by making Buffalo's largest cookie.

他们想打破巴甫洛最大的曲奇纪录。

【小知识】

如果说set/put the record straight，就跟打破记录没多大关系了，它的意思是陈述真相，澄清是非。

She's decided to write her memoirs to set the record straight once and for all.

她决定撰写回忆录以彻底澄清事实。

3 chalk up records

chalk sth up的意思是获(胜)、得(分)，比如：

New world records in the track and field events are chalked up from time to time in the past few years.

近几年来经常出现新的世界田径纪录。

4 create/ establish/ make/ register a new record

She established a new European record in the high jump.

她创造了欧洲跳高的新纪录。

5 beat/ smash/ shatter a previous record

beat、smash和shatter都有打、打破的意思，这几个词是不是比break更激烈更生动呢?

She beat the world record in the three events and entered on her way to two gold medals and a silver.

她在三项竞赛中打破了世界纪录，获得两枚金牌和一枚银牌。

6 surpass all previous records

surpass的意思是超过、优于、胜过，比如：

His time for the 100 meters surpassed the previous world record by one hundredth of a second.

他以0.01秒的优势打破了100米短跑的前世界纪录。