History of Mandarin adaptation of Frère Jacques
Before any Mandarin adaptation, Frère Jacques was already adapted into Cantonese and other Sinitic languages in South East Asia. There is a Cantonese version 打開蚊帳 (Open the Mosquito Net), which is basically about trying to get rid of a mosquito that snuck into the mosquito net. This version existed at least as early as 1835.
打開蚊帳、打開蚊帳。有隻蚊、有隻蚊。快啲攞把扇嚟、快啲攞把扇嚟。撥走佢、撥走佢
In 1926, Frère Jacques was adapted into a anti-warlord song for the Northern expedition, called the National Revolution Song.
The lyrics goes:
打倒列強，打倒列強，除軍閥，除軍閥，國民革命成功，國民革命成功，齊歡唱！齊歡唱！
Defeat imperialists. Defeat imperialists. Get rid warlords. Get rid warlords. VIVA national revolution. VIVA national revolution. Celebrate! Celebrate!
This version was like the de facto National Anthem of the CKS led ROC government between 1927 and 1930.
Half way through the Northern expedition, Chiang Kai-shek broke off with Wang Jin-wei and the CCP. So his frienemies (some says it was Feng Yu-hisang in 1930) changed the lyrics to:
打倒老蔣，打倒老蔣，除軍閥！除軍閥！革命一定成功，革命一定成功，齊歡唱！齊歡唱！
Defeat Chiang baldie. Defeat Chiang baldie. Get rid warlords. Get rid warlords. VIVA revolution. VIVA revolution. Celebrate! Celebrate!
After CKS fled to Taiwan with tail between his legs, the CCP readapted the song to persecute land owners.
打倒土豪，打倒土豪，分田地！分田地！我們要做主人，我們要做主人，齊歡唱！齊歡唱!
Defeat landlords. Defeat landlords. Divide the land. Divide the land. We are the masters. We are the masters. Celebrate! Celebrate!
In 1965, the KMT readapted it to an anti-communist military song.
打倒共匪，打倒共匪 保國家，保國家， 固守台灣基地，完成反攻大陸， 真高興，真高興。
Defeat the communist bandits. Defeat the communist bandits. Save the country. Save the country. Defend our base in Taiwan. Accomplish retaking the mainland. We’re so glad. We’re so glad.
As to how the current version of two tigers came about…
A likely origin story is that around the time the KMT was pushing for their National Revolution Song to become the national anthem, the tune become popular, and for some reason, people started attaching the translated lyrics to Three Blind Mice to the tune of Frère Jacques.
Translation of Three Blind Mice
三隻盲鼠，三隻盲鼠。瞧它們跑，瞧它們跑。它們都在追趕那個農婦。她用刀切了它們的尾巴。你見過這樣的情景嗎？如三隻盲鼠。
To make the lyrics fit the tune better it was first shortened to
三隻盲鼠，三隻盲鼠。瞧它們跑，瞧它們跑。一隻没有尾巴，兩隻没有耳朵。真奇怪。真奇怪。
Three Blind Mice. Three Blind Mice. See how they run! See how they run! One’s missing a tail. The other two are missing their ears. So strange. So strange.
Basically the farmer’s wife was cut from the song, but the effect of her cutting off their tails stayed.
Then someone thought it flowed better if the number of mice missing a tail and ears matched, and changed the song to two blind mice.
兩隻盲鼠，兩隻盲鼠。瞧它們跑，瞧它們跑。一隻没有尾巴，一隻没有耳朵。真奇怪。真奇怪。
Then 盲鼠 blind mice was eggcorned to 老虎 tiger, and with some slight alteration, the current version was born sometime in late 1920s. The missing eyes part in the current version probably hints at the Three Blind Mice origin.
兩隻老虎，兩隻老虎。跑得快，跑得快。一隻没有眼睛，一隻没有尾巴。真奇怪。真奇怪。
The earliest written record of 兩隻老虎 might be a 1943 Chiang Ching-kuo speech in Chungking. If the tigers version was created in late 1920s, then CKS would have learned the song in his teens.
