A measurement of the time-dependent CP-violating asymmetry in Bs0 ->phi phi = 7 TeV in 2011, 8 TeV in 2012 and 13 TeV in 2015 and 2016, a signal yield of around 9000 Bs0 ->phi phi decays is obtained. The CP-violating phase phi sss over bar is measured to be -0.073 +/- 0.115(stat) +/- 0.027(syst) rad, under the assumption it is independent of the helicity of the phi phi decay. In addition, the CP-violating phases of the transverse polarisations under the assumption of CP conservation of the longitudinal phase are measured. The helicity-independent direct CP-violation parameter is also measured, and is found to be |lambda| = 0.99 +/- 0.05(stat) +/- 0.01(syst). In addition, T-odd triple-product asymmetries are measured. The results obtained are consistent with the hypothesis of CP conservation in b over bar -> s over bar ss over bar transitions. Finally, a limit on the branching fraction of the B-0 -> phi phi decay is determined to be Bmml:mfenced close=")" open=(B0 ->phi phi 2.7x10(-8) at 90% confidence level.