Originally posted by Krosis:

somehow swimming for more than a few seconds starts killing me (?????????).

others have helped with the general strat so i want to point this out,

You do not go swimming without food buffs and full stamina as when you get to 0 stamina you will start to take damage.

side note: first boss is not fast, get a little distance and you can walk him around, kite him around the big stones and put some arrows in him when you can, also shield is very nice to have in this fight to swap to.

Good luck.