Phytohydra's ability doesn't prevent damage. Damage that can't be prevented will still be replaced by +1/+1 counters being put on Phytohydra.

If another effect would prevent damage from being dealt to Phytohydra or replace it with something else, Phytohydra's controller chooses which effect to apply first.

If Phytohydra blocks or is blocked by a creature with first strike or double strike, Phytohydra will get the counters during the first-strike combat damage step before it deals its own combat damage during the second combat damage step.