The easiest way for a non-outsider non-good-subtype cleric to cast the 8th-level Sor/Wiz spell last judgment [necro] (Book of Exalted Deeds 102) is likely by first casting the 4th-level Clr spell lesser holy transformation [trans] (Spell Compendium 116) that for 1 round/level changes the caster into a protectar (Miniatures Handbook 66) and, in addition to other effects, the caster's "creature type changes to outsider (good)."
Other methods—like levels in a prestige class that changes the potential caster's type and subtypes like 5 levels of divine disciple (Player's Guide to Faerûn 51-2) or 10 levels (and no spellcasting!) of incandescent champion (Magic of Incarnum 115-21), or, instead, just wholesale becoming a bariaur (Book of Exalted Deeds 165-7) using the Ritual of Vitality (Savage Species 150)—are usually changes persisting forever. Other spells can temporarily change the subject's type to outsider but don't add the subtype good.
For a non-outsider wizard or sorcerer lacking the good subtype, creating or commissioning a custom staff of last judgment (DMG 287) (300 gp +1,800 gp/charge; 4 lbs.) is likely the easiest way to cast the spell, the spell's components probably subsumed in the staff's creation. Ask first, though, as a DM may rule that a creature wishing to cast the spell last judgment from a staff must still be an outsider with the good subtype, the effects of the celestial component on magic items being, of course, unmentioned by the Dungeon Master's Guide. (Instead, in a pinch, a scroll of last judgment could be used (it also needing DM approval regarding the spell's unusual component), but the reader uses the scroll's likely (ahem) abysmal saving throw DC instead of the reader's own ability scores as one does with a magic staff.)