Daily event quest list (they reset at 00:00 JST):
Monday 月
種火集め ‹三騎士編› - Ember Gathering (Three Knights Edition) – Saber, Lancer, and Archer EXP cards
宝物庫の扉を開け – Open the Door of the Treasure Vault – QP
Tuesday 火
種火集め ‹四騎編› - Ember Gathering (Four Horsemen Edition) – Rider, Caster, Assassin, and Berserker EXP cards
三騎士と対決 – Showdown with Three Knights – Saber, Lancer, and Archer Ascension items
Wednesday 水
宝物庫の扉を開け – Open the Door of the Treasure Vault – QP
四騎と対決 – Showdown with Four Horsemen – Rider, Caster, Assassin, and Berserker Ascension items
Thursday 木
種火集め ‹三騎士編› - Ember Gathering (Three Knights Edition) – Saber, Lancer, and Archer EXP cards
モンスター狩り ‹三騎士編› - Monster Hunt (Three Knights Edition) – Saber, Lancer, and Archer Skill Reinforcement Items
Friday 金
種火集め ‹四騎編› - Ember Gathering (Four Horsemen Edition) – Rider, Caster, Assassin, and Berserker EXP cards
モンスター狩り ‹四騎編› - Monster Hunt (Four Horsemen Edition) – Rider, Caster, Assassin, and Berserker Skill Reinforcement Items
Saturday 土
宝物庫の扉を開け – Open the Door of the Treasure Vault – QP
黎明の手狩り ‹オール編› - Gathering at Daybreak – all seven classes’ EXP cards
Sunday 日
絆の戦い – Bond Battle – easier to increase Bond EXP
マスター訓練 – Master Training – can gain large amounts of Master EXP
Note: the 10 AP Master Training gives you ~1100 EXP, the 20 AP ~8300 EXP, and the 40 AP ~34,000 EXP. Rewards scale higher than the AP costs do, aka it's very worth it to do them as high as you can go. (Though in the case of master exp, don't do a higher level one if you'll level up more than once as you'll lose out on max AP refills.)
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