Scrape through
Definition 1 of 1
Pro Tip 1/3Effort Implied
The phrase suggests that success was achieved with great effort and usually at the last moment. 
He scraped through his driving test after many failed attempts.
Pro Tip 2/3Bare Minimum
It implies doing just enough to meet the basic requirements, without excelling. 
She managed to scrape through the interview with the minimum required score.
Pro Tip 3/3Slight Success
Offers a sense of relief or narrow escape from failure, and not a robust success. 
Despite being ill, he scraped through the marathon just before the cutoff time.