The problem must be with the wood subfloor and if you don’t want to rip up your floor, the only way is to open the ceiling below and tighten the
plywood to the joists.
i guess the grout around the tiles must be cracking. if so then filling the gaps with caulk or silicon might just work (worth trying a small area).
if not then it’s likely that water has got in and the sub floor started to deteriorate. in this case i don't see any real alternative to ripping up and starting again.
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