The evolution of nuclear magic numbers at extremes of isospin is a topic at the forefront of contemporary nuclear physics. $N=50$ is a prime example, with increasing experimental data coming to light on potentially doubly-magic $^{100}$Sn and $^{78}$Ni at the proton-rich and proton-deficient extremes, respectively. Experimental discrepancies exist in the data for less exotic systems. In $^{86}$Kr the $B(E2;2^+_1rightarrow0^+_1)$ value - a key indicator of shell evolution - has been experimentally determined by two different methodologies, with the results deviating by $3sigma$. Here, we report on a new high-precision measurement of this value, as well as the first measured lifetimes and hence transition strengths for the $2^+_2$ and $3^-_{(2)}$ states in the nucleus. The Doppler-shift attenuation method was implemented using the TIGRESS gamma-ray spectrometer and TIGRESS integrated plunger (TIP) device. High-statistics Monte-Carlo simulations were utilized to extract lifetimes in accordance with state-of-the-art methodologies. Lifetimes of $tau(2^+_1)=336pm4text{(stat.)}pm20text{(sys.)}$ fs, $tau(2^+_2)=263pm9text{(stat.)}pm19text{(sys.)}$ fs and $tau(3^-_{(2)})=73pm6text{(stat.)}pm32text{(sys.)}$ fs were extracted. This yields a transition strength for the first-excited state of $B(E2;2^+_1rightarrow0^+)=259pm3text{(stat.)}pm16text{(sys.)}$ e$^2$fm$^4$. The measured lifetime disagrees with the previous Doppler-shift attenuation method measurement by more than $3sigma$, while agreeing well with a previous value extracted from Coulomb excitation. The newly extracted $B(E2;2^+_1rightarrow0^+_1)$ value indicates a more sudden reduction in collectivity in the $N=50$ isotones approaching $Z=40$.
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