Pretty straightforward. Looking for a translation, Munster dialect preferred but not necessary, of the phrase:

... the "Big Bear" in questions being Ursa Major.

So far, my best guess is something like "Ordú Draoi na Béar Mór" which is nice in being decently pronounceable for English speakers, which is important for the intended usage.

And if I could trouble for just one more, would as in the "Universal Life Church" be "Uilíoch Saol Druí"? or would perhaps something like "Ord Druí Uilíoch Beatha" sound better to the native ear?

Can I get any assistance with these translations, as I am a near-complete beginner?

in advance!

It's difficult to create phrases like that in another language without knowing the grammar, especially with phrases like this which involve the genitive case.

For the first one, I think this is the approach you need:
Ordú Draoithe an Bhéir Mhóir
"Order of [the] Druids of the Big Bear"
The first "the" isn't there in the Irish, but the Irish can be read in English as being with or without that "the".

and for the second one, there are two possibilities, depending on which noun you choose for "life":
Draoithe an tSaoil Uilíoch
Draoithe na Beatha Uilíche
"Druids of the Universal Life"
The two choices are different grammatically, because saol is masculine in grammatical gender, and beatha is feminine. People will have different opinions about which noun to use. One thing to keep in mind is that saol can also mean "world", so that choice may be ambiguous.

Definitely wait for others to chime in, because genitive forms (and especially double genitives) can be tricky, and it would e better to have someone check what I've done.

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I'm not a native (or entirely fluent) speaker, so be sure to wait for confirmations/corrections, especially for tattoos.

Which is why I never comment on these. Sorry can't help.

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It is recommended that you always wait for three to agree on a translation.
I speak Connemara Irish, and my input will often reflect that.
I will do an mp3 file on request for short translations.
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Ordú is "order" as in "a command". Here, I think the meaning is more like "a religious order", which would be ord.

Modelling on other compounds such as ord ridireachta "an order of knights", I'd suggest:

Ord Draíochta an Bhéir Mhóir (CO)
"Druidic Order of the Big Bear


I think both of those work.

I don't know if this pans with other people's understanding but I look on saol as more like a place, based on the background Christian assumption that you come into this life from another plane and that you will go to another place in an afterlife (rather than being reborn on this earth or in this universe as in reincarnation).

Beatha is more a life force and the state of having that life force (being alive) or not having that life force (being dead).

But as I said, other people's interpretations may differ ...

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Múinteoir Gaeilge - Irish Teacher
My "specialty" is Connemara Irish, particularly Cois Fhairrge dialect, but I can also speak Ulster and Munster Irish with native-level pronunciation.
Is fearr Gaeilge ḃriste ná Béarla cliste, cinnte, aċ i ḃfad níos fearr aríst í Gaeilge ḃinn ḃeo na nGaeltaċtaí.
Gaeilge Chonnacht (GC), go háraid Gaeilge Chois Fhairrge (GCF), Gaeilic Uladh (GU), Gaelainn na Mumhan (GM), agus Gaeilge an Chaighdeáin Oifigiúil (CO).

Thank you all for the help! As always, you are all an indispensable resource to those of us still learning /trying to learn.