Beastmaster

The Beastmaster Archetype from the APG, grants the Addition Feat of Magic Hide (ranger). Magic Hide has the prerequisites of animal companion and warden spells. I assume we can Ignore the Warden Spells prerequisite?

Hmmm, that's a bit odd but I think the idea here is that you have any of the Focus Spells from that Archetype to count as a pre-req especially since most of them were more or less lifted directly from the Ranger or Druid Class Feat lists directly with minor wording tweaks. For the Ranger these are always spelled out as "Warden Spells" but the versions included in the Archetype that simply states "Focus Spell."

It seems to be missing a line that indicates that your Focus Spells gained from the Archetype should be treated as "Warden Spells" for these purposes.

Yeah there is a bit that says any Warden Spells granted are considered Beastmaster focus spells.

BUT the Prerequisite precludes you from getting a warden spell in the first place (hence the "pre" of prerequisite part). Im just gonna assume its bad wording again.

Found this

Some archetypes allow other feats beyond those in their entry. These are typically class feats, such as fighter feats that represent certain combat styles. The list of additional feats includes the feat's name, its level, and the page number where it appears. You can take the feat as an archetype feat of that level, meaning it counts toward the number of feats required by the archetype's dedication feat. When selected this way, a feat that normally has a class trait doesn't have that class trait.

Click here for the full rules on Additional Feats.

Note: Warden spells granted by these feats are beastmaster focus spells for you.

https://2e.aonprd.com/Archetypes.aspx?ID=50

Again bad wording, If a Warden Spell is a "Beastmaster Focus Spell" then I cant get "Magic Hide Feat" because the prerequisite is "Warden Spells" not Beastmaster Spells.
I wouldnt be so pedantic about it except it specifically says

"Sometimes an archetype feat grants another feat, such as the alchemist’s Basic Concoction. You must still meet the prerequisites of the feat you gain in this way."

But again Im just gonna ignore it.

I feel like that note would have made much more sense if only they swapped the words "Warden" and "Beastmaster" in which case it would have eliminated this issue altogether since "Beastmaster Spells" isn't a pre-req for anything at all.

I think what is meant that you need to first have the Heal Animal beastmaster spell, after which you can select the other beastmaster spells. Same as with the ranger, where you need either Heal Animal or Gravity weapon before you can take any of the others.