A logline should be 1 sentence and ideally no more than 40 words (but preferably as few as possible). Check out the formula tab for help with how to format a logline.
As CraigDGriffiths said, specificity is good. Deep history - what's that? Tragedy - what happened? Vengeance - on who? Love of his life - who/what's this? Has he just lost the love of his life or everything?
Also, currently you seem to have two goals. 1) seeking vengeance 2) protecting his family (although I'm confused by who he is protecting his family from). Which is his primary goal?
Removing certain words can easily reduce your logline down. "is hit with tragedy" - you've told us he loses everything, a reader would understand that's tragic. "a deep history that he tries to leave behind" - be more specific e.g. "ex-con" or "recovering alcoholic" or "retired hitman". All of those would hint at a history that he might want to leave behind and can also give us clues as to the nature of the story. For example - if you said "ex-con" we could assume that his criminal past is catching up with him and his old friends might be the antagonistic forces working against him.
Hope this helps. I look forward to the next draft.