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Hadn't realised you didn't need to clear the boss again, I expect I can clear second boss without too must frustration in that case, unlock the grapple and explore whatever it is I've missed. I think there's deep sea boots required to access things I've seen glowing under water too.
The past part about this game for me is that it moves so quick and so smooth, I suspect its a solid 60fps despite being able to move at maybe 3x the speed of cod? All down to the compartmentalised level layout of course.
I haven't reached the second boss yet, still exploring.
You don't have to redo the first boss again, you can run straight too the portal although I think it's a good idea to pick up a few health upgrades first. There's a proficiency pickup at the start of 2 that takes you up to level 5 I think.
Edit: also stuff you unlock in the second biome (guns etc.) can now drop in the first biome, which can make things easier.