I got permission from
Codraroll to compile a list of the Legendaries' desired Natures and Hidden Powers. I'll probably update this several times so check back later.
EDIT: It's done.
Raikou
Tiers - UU, OU, Doubles
Natures - Timid (all Tiers)
Hidden Power - Grass (UU for mandatory coverage slashed with Ice on Specs set), Ice (UU for mandatory coverage slashed with Grass on Specs set, OU for mandatory coverage, Doubles for mandatory coverage)
Set Info -
http://www.smogon.com/dex/xy/pokemon/raikou
Notes - N/A
Entei
Tiers - UU, OU
Natures - Adamant (all Tiers)
Hidden Power - N/A
Set Info -
http://www.smogon.com/dex/xy/pokemon/entei
Notes - Requires Extreme Speed from event to be completely viable.
Suicune
Tiers - UU, OU, Doubles
Natures - Bold (all tiers), Modest (Doubles)
Hidden Power - N/A
Set Info -
http://www.smogon.com/dex/xy/pokemon/suicune
Notes - N/A
Lugia
Tiers - Ubers
Natures - Bold, Impish
Hidden Power - N/A
Set Info -
http://www.smogon.com/dex/xy/pokemon/lugia
Notes - N/A
Ho-Oh
Tiers - Ubers
Natures - Adamant, Impish
Hidden Power - N/A
Set Info -
http://www.smogon.com/dex/xy/pokemon/ho-oh
Notes - Requires Regenerator from Dream Radar to be completely viable.
Regirock
Tiers - NU, RU
Natures - Impish (NU), Careful (RU)
Hidden Power - N/A
Set Info -
http://www.smogon.com/dex/xy/pokemon/regirock
Notes - N/A
Regice
Tiers - NU
Natures - Calm
Hidden Power - N/A
Set Info -
http://www.smogon.com/dex/xy/pokemon/regice
Notes - N/A
Registeel
Tiers - RU
Natures - Calm, Careful
Hidden Power - N/A
Set Info -
http://www.smogon.com/dex/xy/pokemon/registeel
Notes - N/A
Latias
Tiers - OU, Ubers
Natures - Timid (all), Bold (OU)
Hidden Power - Fire (OU for optional coverage), Fighting (OU for optional coverage but is impossible to get)
Set Info -
http://www.smogon.com/dex/xy/pokemon/latias
Notes - Defog is required for non-Mega sets to be completely viable. Analysis does not have Mega Latias sets or Ubers sets since Soul Dew was recently released. HP Fighting is also impossible to get in Gen VI.
Latios
Tiers - OU, Ubers
Natures - Hasty (OU), Timid (all)
Hidden Power - Fire (OU for optional coverage), Fighting (OU for optional coverage but is impossible to get without transfer)
Set Info -
http://www.smogon.com/dex/xy/pokemon/latios
Notes - Defog is required for non-Mega sets to be completely viable. Analysis does not have Mega Latios sets or Ubers sets since Soul Dew was recently released. HP Fighting is also impossible to get in Gen VI.
Kyogre
Tiers - Ubers
Natures - Modest, Timid
Hidden Power - Ground (optional coverage for Calm Mind set)
Set Info -
http://www.smogon.com/dex/xy/pokemon/kyogre
Notes - N/A
Groudon
Tiers - Ubers
Natures - Adamant, Naughty, Jolly, Careful
Hidden Power - N/A
Set Info -
http://www.smogon.com/dex/xy/pokemon/groudon
Notes - N/A
Rayquaza
Tiers - Ubers, AG (Mega Rayquaza only)
Natures - Adamant, Naughty, Jolly, Naive
Hidden Power - N/A
Set Info - Analysis is outdated. Check Ubers Subforum.
Notes - Dragon Ascent is legal in Ubers, but you are not allowed to Mega Evolve Rayquaza outside of AG.
Deoxys-D
Tiers - Ubers
Natures - Calm, Careful
Hidden Power - N/A
Set Info -
http://www.smogon.com/dex/xy/pokemon/deoxys-defense
Notes - N/A
Deoxys-N
Tiers - Ubers
Natures - Timid
Hidden Power - Fire (optional coverage)
Set Info -
http://www.smogon.com/dex/xy/pokemon/deoxys
Notes - It sucks so don't use it ever.
Deoxys-A
Tiers - Doubles, Ubers
Natures - Naive (all Tiers), Rash (all Tiers)
Hidden Power - Fire (Ubers for optional coverage)
Set Info -
http://www.smogon.com/dex/xy/pokemon/deoxys-attack
Notes - N/A
Deoxys-S
Tiers - Ubers
Natures - Jolly, Timid
Hidden Power - N/A
Set Info -
http://www.smogon.com/dex/xy/pokemon/deoxys-speed
Notes - N/A
Uxie
Tiers - NU
Natures - Bold, Impish, Relaxed, Timid
Hidden Power - N/A
Set Info -
http://www.smogon.com/dex/xy/pokemon/uxie
Notes - N/A
Mespirit
Tiers - NU
Natures - Timid
Hidden Power - Fire (mandatory coverage for Scarf set)
Set Info -
http://www.smogon.com/dex/xy/pokemon/mesprit
Notes - N/A
Azelf
Tiers - UU, OU
Natures - Jolly (all Tiers), Timid (all Tiers), Naive (all Tiers), Hasty (OU)
Hidden Power - N/A
Set Info -
http://www.smogon.com/dex/xy/pokemon/azelf
Notes - N/A
Dialga
Tiers - Ubers
Natures - Modest, Calm
Hidden Power - N/A
Set Info -
http://www.smogon.com/dex/xy/pokemon/dialga
Notes - N/A
Palkia
Tiers - Ubers
Natures - Timid, Calm
Hidden Power - N/A
Set Info -
http://www.smogon.com/dex/xy/pokemon/palkia
Notes - N/A
Heatran
Tiers - OU, Doubles, Ubers
Natures - Timid (OU, Doubles), Modest (OU, Doubles), Calm (OU, Ubers)
Hidden Power - Ice (OU/Doubles for optional coverage)
Set Info -
http://www.smogon.com/dex/xy/pokemon/heatran
Notes - Offensive sets with Timid or Modest run Stone Edge for Talonflame and Charizard Y, so try to get a good Attack IV.
Regigigas
Tiers - NU
Natures - Adamant
Hidden Power - N/A
Set Info -
http://www.smogon.com/dex/xy/pokemon/regigigas
Notes - N/A
Giratina-A
Tiers - Ubers
Natures - Careful, Impish
Hidden Power - N/A
Set Info -
http://www.smogon.com/dex/xy/pokemon/giratina
Notes - N/A
Giratina-O
Tiers - Ubers
Natures - Adamant, Rash
Hidden Power - N/A
Set Info -
http://www.smogon.com/dex/xy/pokemon/giratina-origin
Notes - Some sets need Defog to be completely viable.
Cresselia
Tiers - RU, UU, OU, Doubles
Natures - Bold (RU, UU, OU), Calm (Doubles), Sassy (Doubles), Modest (Doubles), Timid (RU, UU)
Hidden Power - Ground (Doubles for optional coverage), Fire (OU for optional coverage)
Set Info -
http://www.smogon.com/dex/xy/pokemon/cresselia
Notes - N/A
Cobalion
Tiers - RU, UU, OU (viable, but no sets are currently on the Analysis)
Natures - Timid (RU and UU), Jolly (all Tiers), Naive (UU)
Hidden Power - Ghost (RU for mandatory coverage, UU for coverage)
Set Info -
http://www.smogon.com/dex/xy/pokemon/cobalion
Notes - Some sets run Volt Switch even if Jolly, so try to get a good Special Attack IV.
Terrakion
Tiers - OU, Doubles, Ubers
Natures - Jolly (all Tiers), Naive (OU)
Hidden Power - Ice (OU for optional coverage with Naive Nature)
Set Info -
http://www.smogon.com/dex/xy/pokemon/terrakion
Notes - N/A
Virizion
Tiers - RU, UU
Natures - Timid (all Tiers), Jolly (all Tiers)
Hidden Power - Fire (RU for mandatory coverage slashed with Rock on Calm Mind set), Rock (RU for mandatory coverage slashed with Fire on Calm Mind set)
Set Info -
http://www.smogon.com/dex/xy/pokemon/virizion
Notes - N/A
Tornadus-I
Tiers - UU
Natures - Jolly, Naive, Timid
Hidden Power - N/A
Set Info -
http://www.smogon.com/dex/xy/pokemon/tornadus
Notes - N/A
Tornadus-T
Tiers - OU
Natures - Naive, Timid
Hidden Power - N/A
Set Info -
http://www.smogon.com/dex/xy/pokemon/tornadus-therian
Notes - N/A
Thundurus-I
Tiers - OU, Doubles, Ubers
Natures - Naive (OU), Timid (all Tiers), Modest (Doubles)
Hidden Power - Ice (OU for mandatory coverage on most sets, Doubles for mandatory coverage on all sets, Ubers for optional coverage), Flying (OU for coverage slashed with Ice on the Nasty Plot set)
Set Info -
http://www.smogon.com/dex/xy/pokemon/thundurus
Notes - While HP Flying is possible to obtain, Gen VI mechanics force using suboptimal IV spreads that cost a point of Speed.
Thundurus-T
Tiers - OU
Natures - Timid
Hidden Power - Flying (mandatory coverage)
Set Info -
http://www.smogon.com/dex/xy/pokemon/thundurus-therian
Notes - N/A
Reshiram
Tiers - Ubers
Natures - Naive, Rash, Timid, Modest
Hidden Power - N/A
Set Info -
http://www.smogon.com/dex/xy/pokemon/reshiram
Notes - N/A
Zekrom
Tiers - Ubers
Natures - Lonely, Naughty
Hidden Power - N/A
Set Info -
http://www.smogon.com/dex/xy/pokemon/zekrom
Notes - N/A
Landorus-I
Notes - Don't bother, as it's unviable without Sheer Force. SR for Landorus-T's nature.
Landorus-T
Tiers - OU, Doubles, Ubers
Natures - Adamant (all Tiers), Impish (OU, Ubers), Jolly (OU, Ubers
Hidden Power - Ice (Ubers optional coverage)
Set Info -
http://www.smogon.com/dex/xy/pokemon/landorus-therian
Notes - N/A
Kyurem
Tiers - UU, OU
Natures - Hasty (UU), Mild (UU), Modest (all Tiers), Timid (UU).
Hidden Power - N/A
Set Info -
http://www.smogon.com/dex/xy/pokemon/kyurem
Notes - N/A
Kyurem-W
Tiers - Ubers
Natures - Modest, Timid
Hidden Power - N/A
Set Info -
http://www.smogon.com/dex/xy/pokemon/kyurem-white
Notes - N/A
Kyurem-B
Tiers - OU, Doubles
Natures - Adamant (Doubles), Naive (OU), Naughty (OU), Lonely (all Tiers), Mild (OU), Modest (Doubles), Rash (OU),
Hidden Power - Fire (OU for optional coverage)
Set Info -
http://www.smogon.com/dex/xy/pokemon/kyurem-black
Notes - N/A