Критично ли с грамматической точки зрения писать "show must go on" без "the" в начале?

Критично. The Show Must Go On. Это не проходной, рядовой заголовок.
Это известная, растиражированная, легендарная фраза, которая многократно воспроизводилась и узнается в таком виде.

( From Wikipedia, the free encyclopedia)
"The show must go on" is a well-known phrase in show business, meaning that regardless of what happens, the show must still be put on for the waiting patrons. This is an abbreviation of what many believe to be the true saying which is "The show must go on, otherwise we'll have to give them their money back". This is a reflection on the entertainment industry which is perceived as insincere and shallow.

The Show Must Go On may also refer to:
The Show Must Go On (film), a 2007 Korean film
The Show Must Go On (2010 film), a Croatian film directed by Nevio Marasović
The Show Must Go On (play), a 1991 Japanese play by Koki Mitani
"The Show Must Go On" (ER), the final episode of the 11th season of the American drama ER
"The Show Must Go On" (The Nanny), an episode of the television series The Nanny
"The Show Must Go On" (McLeod's Daughters), a musical episode of the highly popular Australian drama, McLeod's Daughters
"The Show Must Go On", an episode of One Tree Hill (TV series)
Music"The Show Must Go On" by the band Queen from their 1991 album
"The Show Must Go On" (Pink Floyd song)
"Why Must the Show Go On?", a song written by Noël Coward
"The Show Must Go On" (Chicago song), by the band Chicago
"The Show Must Go On", a song by the English progressive band Nirvana

Английский не очень удобный язык для тату - все эти артикли, вспомогательные глаголы.. .

можно, если show - в общем смысле, не какое-то конкретное
для краткости и экономии места, например, в заголовках артикли часто опускаются