From WP, AK, Ifrit HM. They can be done with AF1 + Weapon from story quest.

If you ask a question, "How do I know?" then here is my answer. Try all dungeons, including option one, and up to final story one. If you are not leveling with FATE and know how to rotate your skill, then you are ready.

The main problem is not gear, but skill especially with the FATE grind all over the place.

Garuda HM has dps check, e.g. easy one (plume b4 reckoning) and harder one (twin sisters)

Titan HM has dps check (heart + dmg after heart before unhealable)

p.s. Ifrit HM also has a dps check, but it is too easy if you have a caster for meteo in party, otherwise it is a real dps check.