Generic Offensive Physical Gears

Below are noteworthy custom gears applicable to boosting physical damage output. Note that God Items and MVP Cards are excluded from the list.

Amdusias Boots has no slot but offers great AGI and ASPD in a slot that typically has no offensive stats
Bradium Brooch is a strong accessory with 5 flee with some ASPD, better than Flopping Fish but weaker than Quah-Nomag Gloves, yet this is class generic
Bradium Ring is good generic accessory with STR and ATK % bonus, usable by all classes
Crown of Deceit is a cheaper but weaker option to Hermode Cap
Dreamstone Charm is weaker than Menacing Doll but has no downside of generic ATK/MATK boost
Flopping Fish is a generic accessory for ASPD
Hermode Cap is a fantastic general offensive headgear slot with great ASPD and generic damage boost
Jasper Crest is an option for HP healing without using Hunter Fly related builds, but it's not as consistent
Lounge Suit is an option when defense is not a concern, and you want to attack/cast faster while having a card slot
Menacing Doll offers good boosts while keeping a card slot, but it can be a drain on your resource to maintain it
Plane Hat is great for ranged attackers for flee characters to boost ASPD with huge defensive sacrifice
Power Symphony is one of the best offensive accessories giving 4 STR in accessory and giving further damage with Kihop in party setting, but it is from an endgame MVP dungeon
Skeleton Hood is a good all-around flee headgear with flee while balancing some offensive stats, but lacks a slot
Ring of Angel Whisper grants access to Lv 2 Impositio Manus, which can give more ATK power than any other accessory in the right circumstance especially in a party without a Priest

Physical Based Cards

Armed Guard Soheon Card generally gives less damage than usual 20% damage cards, but if your build needs the ASPD then this card can be useful
Fighter Scaraba Card is one of the best generic

Critical Based Gear

Renown Archer's Glove is a slotted accessory geared towards boosting CRIT damage
Avian Wings should be mentioned again since it has standalone CRIT without cards in armor slot
Hat of Fortune sacrifices CRIT for more CRIT damage, if your build has excess CRIT and can use more damage
Vesper Core 5 is a decent cheap option to get a bit of CRIT and CRIT damage without cards
Wickebine Ears offer both flee and crit which is generally the desired stats of crit based builds

Critical Based Cards

Angra Mantis Card is one of the best cards for getting CRIT damage when you have sufficient CRIT already to not require Chung E card
Constant Card is useful to offer balance of CRIT and CRIT damage, even for non-gunslingers
Fallen Druid Card sacrifices HP but also provide CRIT in a rare slot that does not usually provide offensive stats