I'm, uh, not entirely sure how Anna Navarre counts as the "third boss" in DX1; that would be Walton Simons, inasmuch as anybody in DX1 qualifies as a "Boss Fight".
The fight with Anna in UNATCO can only really have one outcome, but you're given plenty of options to tangle with her in different ways prior to that - you can ambush her in the 747 (place LAMs correctly and she's vapourised in the middle of your conversation with Lebedev!), and if you choose to fight her in Battery Park then you have plenty of options for hit-and-fade attacks or bypassing her and trying to sneak out through the ventilation shafts.
Gunther can only really be defeated by shooting him until he retreats or dies, but you can just turn invisible and hack the computer without him being any the wiser.
Walton Simons provides you all sorts of ways to deal with him in the Ocean Lab; you can set environmental traps for him (electrified rails, explosive/toxic barrels, luring him near the transgenic creatures), and you have many ways of fighting him in a stealthy manner (or once again, bypassing him) - some enterprising players have even managed to get him to drown himself while pursuing them! The final confrontation with Simons at Area 51 is a lot more straightforward, but you do have the amusing option of using Aggressive Defence System to get him to blow himself up with his own hand grenades.
The bigger issue, though, is that, barring Anna Navarre, none of the DX1 fights were really meant to be classical boss fights where you're locked in a room with them and their death is the only way to progress. They were hostile encounters with enemies who happened to be particularly dangerous, and much like the rest of the game, you were given a wide range of options to defeat, bypass, or simply ignore them. They certainly didn't get bullshit magic invulnerability to half of your most effective attacks - if you wanted to ignominiously blast Anna out of existence with a single GEP rocket, then that's what happened - she'd get blown up and die instantly, much as you'd expect anybody who's just been hit with a high-explosive rocket would. Barrett, by contrast, just stands there as if nothing has happened to him and keeps on shouting his stupid taunts. He might as well have been given a big glowing health bar.