oh i didnt know you main shyvana since you have only a whopping 0 shyvana games on your account.
shyvana is a fighter/juggernaut/duelist and as such, you cant build two fully offensive items first. devourer is a must, so your next item has to have at least some sort of defensive capabilities. last but not least, botrk is just a relatively weak item right now and even last season there were better alternatives. it is still good lategame as a situational item vs strong frontliners tho. i sometimes get it fourth or fifth.
my preferred build right now is trinity force second since every single stat it gives except mana is extremely good for shyvana. CDR, movespeed and health function as the defensive portion of the item which doesnt leave you entirely vulnerable. last season i got titanic hydra second since it was cheaper and trinity was still different but now trinity is just so much better. i still see some people get titanic second which is fine and still better than botrk.
the third option i often see is a very defensive followup. deadmans plate (+cloak vs strong ap) is viable too if you have a high lockdown team that wants to fight alot early on (malphite + tf or so).
if you went for any offensive option (trinity, titanic, botrk or rageblade), the third has to be a defensive one, mostly deadmans plate. i saw a guy rush cutlass + randuins for maximum teamfight utility and he only went to teamfight and never dueled and it was very good too.
now, getting more than one or at best 1,5 defensive items is way too much and cripples shyvanas damage. building one armor item is mandatory and if they are full ad or have absurdly high magic damage, you CAN go thornmail/ohmwrecker/locket as a second defensive option (fourth item) against that but if it is avoidable, getting more damage is always better. if you went for the trinity build, you can get steraks gage fourth since it boosts not only your defensive capabilities but also your damage and synergizes absurdly good with trinity. after that, you need more damage.
semi-defensive items are: maw of malmortius, mercurial scimitar, steraks gage, titanic hydra. depending on the situation, all of these are good second or fourth options.
as last item you need, as i mentioned, damage. the highest damage against squishy targets you get from titanic hydra as it gives you flat damage boost to your auto attack and it also allows you to reset your auto attack twice (auto -> Q -> hydra) which, if perfectly executed, allows for a full combo within only 0,9 seconds.
the highest damage against tanks you get from rageblade even tho that is only useful if your team is set up to lock targets down for you while protecting you from the AP burst. then you can really shred any full tank mundo or maokai easily. if your team has more defensive abilities than offensive ones (janna, mundo, shen, braum etc) getting botrk as last item is good because it allows you to isolate and duel targets better while your team peels for themselves.
what shyvana never is, is a tank. she cant tank anything as she doesnt have a single ability aside from her passive that gives her tankyness in any way. she cant absorb cooldowns and she cant prevent enemies from dealing damage. your goal is to always kill the closest enemy you can reach as quickly as you can while avoiding as much cc and damage as possible, maximizing your efficiency.
if you R into the enemy team to "tank", you couldve just played another champion instead.