What's the most accessible translation for 修仙 or 修真? Can I use xiuxian? 
It means taking pills of immortality and cultivate oneself to become an immortal, short for cultivate immortality, can you understand the latter easily if it suddenly appears in English article?
修仙 = cultivate oneself to become an immortal
after become 神仙 or 仙 , one can live outside of the mundane world 吸風飲露，不食五穀 (able to exist and function by using the energy from nature, no need to eat)

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修真 = cultivate oneself to achieve spiritual enlightenment
修真者，借假修真也。道教中，学道修行，求得真我，去伪存真 (remove the fault and keep the truth) 为“修真”。

Edit:
Scripps wrote:

Is there any noun to represent that?

修仙 short for 修練成仙之法 (study and train oneself to become an immortal)
修真 short for 修硏尋得真我之法 (Study and learn to find one's truth self)
If you must use simple terms to describe them, you can call '修仙' as 'immortality seeking' and '修真' as 'truth seeking'