"I best go see what he did to our sentries."
Is it grammaticaly correct?
No, it should be like this. I'd best go (and) see what he did to our sentries. ) If this was dialogue that you heard, you may have just missed the "'d".
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No, it should be like this.
I'd best go (and) see what he did to our sentries.
(In BrE you need "and"; in AmE it can be omitted.)
If this was dialogue that you heard, you may have just missed the "'d". Sometimes it may not be articulated very clearly.