Break cauldrons and sink ships
To be willing to sacrifice everything to obtain one's goals; to refuse to retreat in a life-or-death battle
Neutral
他以破釜沉舟的勇气去参加研究生考试 | Tā yǐ pòfǔchénzhōu de yǒngqì qù cānjiā yánjiūshēng kǎoshì
He went to sit the grad school admissions test with true mettle and spirit
[Source]
战士们毫不畏惧，怀着破釜沉舟的决心，英勇地冲向敌人 | Zhànshìmen háo bù wèijù, huáizhe pòfǔchénzhōu de juéxīn, yīngyǒng de chōng xiàng dírén
The soldiers weren't the least bit afraid. Willing to sacrifice everything, they courageously charged towards the enemy
[Source]
Burn one's bridges
沉舟破釜 (chén zhōu pò fǔ)
舟 (zhōu) is an old word for boat, while 釜 (fǔ) is an old word for kettles/cauldrons/pots
《史记》(Shǐ Jì), or the famous work "Records of the Grand Historian" by 司马迁 (Sī Mǎ Qiān).
Around 205 BC, the Qín (秦, 221 - 207 BC) emperor 秦二世 (Qín Èr Shì) ordered his army of 300,000 to attack the nearby kingdom of Zhào (赵, 476 - 220 BC). The Zhào army was hopelessly outnumbered and unable to resist, and they retreated to the city of 巨鹿 (Jù Lù). Unfortunately, the Qín pursued them and started to lay siege to the city. With no other options, the Zhào king wrote a letter to the king of the kingdom of Chǔ (楚, 770 - 223 BC), asking for their help in defeating their mutual enemy.
The Chǔ king received the letter and immediately ordered the general 宋义 (Sòng Yì) and the lieutenant general 项羽 (Xiàng Yǔ) to lead 200,000 troops to aid the Zhào. The army set out, but when they were halfway to their destination, 宋义 unexpectedly ordered them to stop their journey. For almost 50 days, the army remained in the same location without budging, and because 宋义 himself had plenty of food and drink to consume, the fact that the actual soldiers didn't have adequate provisions fell on deaf ears.
项羽 was livid at the whole situation. He tried to urge his superior officer to continue on to help the Zhào, but 宋义 revealed that he had a different plan: he wanted to wait until the Zhào and the Qín had completely exhausted themselves, then strike and secure an easy victory. This enraged 项羽 even further, and after some more time passed, he decided to take matters into his own hands. He killed 宋义 and took his place as the general of the army, then ordered the troops to move out. (He also wrote a letter to the Chǔ king explaining the situation. The king responded by promoting him.)
As the Chǔ troops got closer to their final destination, 项羽 sent out a small force to cut off the Qín food provisions and offer the Zhào army reinforcements. When the request for more help came, he personally led the rest of his troops across the 漳河 (Zhāng Hé) river and ordered them to eat a hearty meal and put aside three days' worth of provisions. When they were finished, he ordered them to sink the boats that they had used to cross the river, smash the pots and pans they had used for making meals, and burn down the barracks. This demonstrated that the army had no means of retreat and was determined to win the coming battles at all costs.
When the fighting actually began, 项羽's troops surged toward the Qín with unparalleled determination, and after a series of charges, they managed to soundly defeat the enemy and kill or capture many of their generals. In fact, the defeat was so resounding that the Qín never fully recovered their might, and within a few years, the dynasty collapsed.