Animar, Soul of Elements reduces the cost of creature spells, but Rhystic Study appears to be an option cost, I presume even with Animar my opponent would have to pay an additional 1 if he doesn't want me to draw a card?
Rhystic Study's ability means, in relevant part, "...that player may pay 1. If that player doesn't, you may draw a card" (C.R. 117.12a) (and if the player does pay, you don't draw a card). Note that that player chooses whether to pay 1 when Rhystic Study's ability resolves, that is, after the spell in question is cast (C.R. 603.5). Animar's cost reduction has nothing to do with this; Rhystic Study's ability will trigger whenever "an opponent casts a spell", regardless of what was paid to cast that spell (C.R. 603.2).
Shu Yun, the Silent Tempest WUR Voltron Control
Temmet, Vizier of Naktamun WU Unblockable Mirror Trickery
Ra's al Ghul (Sidar Kondo) and Face-Down Ninjas
Brudiclad, Token Engineer
Vaevictis (VV2) the Dire Lantern
Rona, Disciple of Gix
Tiana the Auror
Hallar
Ulrich the Politician
Zur the Rebel
Scorpion, Locust, Scarab, Egyptian Gods
O-Kagachi, Mathas, Mairsil
"Non-Tribal" Tribal Generals, Eggs
The cost for Rhystic Study is entirely separate, and cannot be reduced.
RULES OF MAGIC :
http://magic.wizards.com/en/game-info/gameplay/rules-and-formats/rules