Full combo is any hand with: a level 4 beast-warrior monster, any way of getting to Tri-Brigade Kerass (of the 12 ways to find him that I'm running), and a fire formation spell (that includes the field spell as it counts as fire formation but the bouncing with eagle is unfortunate).
*Summon Eagle with the effect of Kerass
*Eagle bounces your Fire Formation to send Buffalo
*Normal summon any level 4 beast-warrior to summon Tiger King (link with Kerass for whatever you want)
P(Fire Formation≥1)= 70% success. If you think that you can't find enough Fire Formation cards I would recommend adding either one Liang peak or a Terraforming. You can only activate Ingen and Domei once per turn and you need to use Domei for your Eland (searched with Elephant), Liang peak is better than Ingen as it is still very useful even if not fully stacked. (You can still add 1 Ingen if you believe Liang+Terraforming is not enough).
P(Kerass≥1)= 85% success. This success rate includes Tenki as a Tri-Brigade card for obvious reasons searching Fraktall. If you fear God you can increase the rate of Nervall in the deck but I'd like to keep bricks to a minimum (already being Domei and Buffalo whereas Nervall, Sinto, Thoroughblade, Zhuge Kong and Eland being somewhat okay bit not great if drawn). Kerass overall success rate depends on a higher density of monsters not only to be discarded, but also for the banishing effect, meaning that useful extender spells such as monster reborn and Fire Kings cards were dissmissed in favour of less explosivity but a more competent deck. This is also in line with a Zoodiac combo I was playing around with using Ratpier and Barage as starters and an extender but they were inconsistent and didn't have a consistent starting combo.
The Zoodiac units in the Extra are to give Drident multiple materials for pops but if you aren't using her, to send Tiger King to the grave, she only needs one material, therefore you can make more room in the Extra. I wouldn't recommend reducing the number of Thoroughblade unless you do get rid of Chakanine and Tiger Mortar as you cannot access that part of the extra deck without a free Zoodiac summoned off of Tiger King, requiring a higher Zoodiac density.
If I was to change anything maybe I'd add some beast-warrior extenders like Tengu but not much else, for consideration Boar -> Lavalval Exlord or Borreload Savage. Could add more cards for going second such as Bear, Gorilla, Called By The Grave. Maybe you could abuse Saryuja I don't think it's neccessary though. Tri-Brigade Rendezvous for OTK potential.
*I am completely unsure about Heraklinos I haven't tested him whatsoever I just recently put in Daigusto Emeral and with that you can cycle more allowing for a few more summons which I think could enable his addition*