Abilities that trigger when counters are put on a permanent trigger when a permanent enters the battlefield with counters and when a player puts counters on a permanent.

If Bioessence Hydra enters the battlefield at the same time as a planeswalker you control, the loyalty counters that planeswalker will receive won't be counted to determine how many counters Bioessence Hydra enters the battlefield with, but they will cause its last ability to trigger.