Cauldron of Souls and Wickerbough Elder
It enters with 2 -1/-1 counters.


  Wickerbough Elder enters the battlefield with a -1/-1 counter on it.


is equivalent to


  As Wickerbough Elder enters the battlefield, place a -1/-1 counter on it.


Similarly, Persist is also an ability that redefines entering the battlefield (ETB) to add the placement of a counter on the card.

Both are replacement effects that modify the same ETB event, so you apply them in the order of your choice.

For the card in question, the first replacement effect applied redefines ETB to add the placement of a -1/-1 counter. The second replacement effect applied then further redefines ETB to add the placement of a -1/-1 counter. Two counters are now placed as it enters the battlefield.