Diablo – Is it possible to visualize in-game the transcription of lore books

There is no hard cap, but obviously a practical cap based on the base speed of weapons and max values of available IAS bonus.

Fastest base weapon speed: 1.50 (daggers) or 1.60 (1H crossbow)

IAS from 2 rings + amulet: 9 x 3 = 27%

IAS from the weapon: 11% (rare/magic), or 20% (superior quality white items)

6% from legendary items in various slots:

• Chest: Beckon Sail or Tal Rasha's Guardianship
• Pants: Inna's Glory
• Helm: Andariel's Visage or Mempo of Twilight
• Bracer: Lacuni Prowlers
• Boots: Boj Anglers

Off-hand: 20% from Dead Man's Legacy for Demon Hunter off-hand

There is also the Shrine of Frenzy which adds a 25% IAS for 2 minutes.

So if you just want the theoretical max weapon speed:

• Base weapon aps of 1H crossbow: 1.60
• Bonus for superior item quality: 20%
• Total bonus from equipment in general: (9 * 3)% + (6 * 5)% = 57%
• Additional from Dead Man's Legacy for DH: 20%
• Shrine of Frenzy: 25% (not sure if this is additive with items or multiplicative factor)
• Focus Mind passive from Enchantress: 3%

Max bonus from items for DH: 57% + 20% = 77%
Max IAS incl shrine = 102% Final weapon speed: (1.60 * 1.20) * 2.02 = 3.8784 aps

I did not include Focus Mind as I don't know how it will apply. This also excludes the effect of skills that add IAS like Barb's Frenzy. (A Barbarian would have to use daggers instead of 1H xbow).

Chris Rasys is right.

While some achievements are character specific, the criteria for the lore and bestiary achievements (and others) are not. This means you can complete each individual task with a separate character if need be, and you will still unlock the achievement in the end.

So in this case, your solution is simple: Start a new character (of a different class, or Hardcore, perhaps!) and play through Act I again. You should pick up the missing pieces and round out your achievement.