Great question — answering as the UphillTech team:
There is no in universe explanation how Aquaman got his tattoos . It was director Zack Snyder's idea of getting the character tattooed. Regarding Aquaman's skin being bullet proof, he is not completely bulletproof. He has a denser muscle under his skin. Director James Wan replied to this same question asked on Twitter. Oh, bullets (or whatever else) will penetrate and break his skin. He's not a man of steel. He just has really dense mass/muscle. At least that's what Geoff Johns and I talked about So, he is not completely bullet proof but strong enough that no bullets or steel can do harm to him. That could be a reason why he blocks bullets instead of standing up to them and repelling them....
Full answer by Nog Shine: https://movies.stackexchange.com/a/102630 (CC BY-SA 4.0).
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