How does 你的健康都难得到保证，就更别说幸福了 work?
&quot;难得到&quot; is short for &quot;难以得到&quot; (hard to get). It is not a standard phrase

(連)*你的健康都难得到保证，(就)*更别说幸福了

There is a common grammar structure here:

[連 (X) 都 (+ statement) , 更别说 (Y)了]
[even (X) (+ statement) , let alone/ not to mention (Y)]
[even (your health) (cannot be guaranteed/ ensured), let alone/ not to mention (your happiness)]
If your health cannot be guaranteed/ ensured , then it is even less likely that your happiness can be guaranteed

連 is omitted in your sentence
就 can be omitted in your sentence
More example of [連 (X) 都 (+ statement) , 更别说 (Y)了] structure:

連(我)都打不過他, 更别说(你)了
even (I) can't defeat him, let alone (you)
If I can't defeat him, it is even less likely that you can defeat him