I'm trying to describe someone who is mentally and physically strong, but who is also able to show his/her tender side and emotions.
There isn't a single word that describes that combination of qualities, at least that I can think of as a native speaker of American English.
It is perfectly fine to describe it the way you have already:
strong yet not afraid to show his or her emotions.
As mentioned in the comments, the use of the word 'yet' would show that you thought it was a contradiction to be both at once. If you didn't want to express that opinion you could say
strong and not afraid to show emotion
Some other options would be
strong and sensitive
strong, with a high degree of emotional intelligence and awareness
strong physically, mentally and emotionally
In this case English is like a language that doesn't have a word for 'orange'. You would have to say 'red like the setting sun'.