It will get 4 counters.
The word “additional” in “enters the battlefield with N additional counters” is there to make it obvious that several such effects will be cumulative, but it's not actually needed and has no rules meaning.
To see why, let's have two creatures, A and B, each saying “creatures you control enter the battlefield with a +1/+1 counter.” You cast a creature. When it would enter the battlefield, the event is
[Creature enters the battlefield.]
We apply A's replacement effect (we could start with B but the order doesn't matter here). The event becomes
[Creature enters the battlefield with a +1/+1 counter.]
B's replacement effect is still applicable, so we apply it as well:
[[Creature enters the battlefield with a +1/+1 counter] with a +1/+1 counter.]
giving a total of 2 counters. Notice that the effects are independent and each one doesn't know that the other is going to put counters on the creature.
Now to come back to the original situation,
Master Biomancer's replacement effect is not aware that the
Nimbus Swimmer is already going to enter the battlefield with some +1/+1 counters already; it simply applies its own replacement. It computes how many counters it would make the Swimmer enter the battlefield with, comes up with -3, and replaces that with 0 (by virtue of the rule you cite), and finally its gives the modified event [[Nimbus Swimmer enters the battlefield with 0 +1/+1 counters] with 4 +1/+1 counters], giving a total of 4 counters.
Daniel Kitachewsky
L3, Paris, France
Rules Netrep