I used this spreadsheet to crack Research Assistant positions at London School of Economics, Monash University, and University of Glasgow.
Along with this, I focused on staying active on LinkedIn and look out for similar opportunities. I tried to connect with professors abroad, to ask them about any available positions.
Remember that quantity along with quality is the key.
While sending out cold emails, I attached my CV along with a Cover Letter and sometimes a brief Statement of Purpose. It's an informal way of landing great internship and thus, being unique in your writing- runs a long way.
Reach out to me in case of any queries:)