You misread the expression. The first word is not tien (your) but tiens, imperative form of the verb tenir (to hold).
- tiens (2nd person singulal)
- tenons (1st person plural)
- tenez (2nd person plural)
The latter gave the English "Tennis".
So
Tiens bon !
is more like (literally):
Hold "well" or Hold "good"!
Instead of Google translate, I’d recommend DeepL which translates Tiens bon ! to :
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