Translation:Ninety, eighty, seventy, sixty, fifty, forty, thirty, twenty, ten
Assuming you already now how to count to ten in the Korean counting system, you should note some similarities and/or common roots.
Other than that, I did have some tricks in the past, but they were very specific to my own background and knowledge (and more often than not, NSFW).
E.g. 여든, sounds like Joden, jews, in Dutch, one of my home tongues. The number 8 has strong links with the neonazi movement. I guess you can make the missing link between jews and neonazis. Or 마흔, which sounds like My hun (affective shortened form of honey, darling). There was a particular person at the time who was forty years old and that would fit that description.
As you can see, there are several pieces of personal trivia in there that makes it probably useful only to me as a mnemonic.
My best advice is to make similar stories or links, and I can assure you, they will stick.
The first 5 is easy to remember: 열 스물 서른 마흔 쉰. The following tens confuse me, but I noticed that if you know how to count already, you'd see the correlation. 6 = 여섯 = 여 = 예순 7 = 일곱 = 일 = 일흔 8 = 여덟 = 여 = 여든 9 = 아홉 = 아 = 아흔
is there a broken down version of each number? what is added to "set" to make it "seruen" (sorry, not korean keyboard)