The Alchemist is by far may favorite class, so I love any opportunity to discuss them. I haven't played with mythic rules, and I've never played a plague-bringer, but here are my 2 cents on alchemists stuff.
It seems like you have a strong concept and are not going for super optimized which is always a good thing and much more rewarding.
Does your GM allow accelerated drinker to apply to extracts as well as potions? (since it really should) both thematically and since the alchemist already struggles with action economy.
Has your GM banned Full Pouch? I see that they have not done so with Alchemical Allocation... which they will learn to regret (be prepared for them to do away with it). But if not, and you plan to heavily utilize AA, then invest in a 2nd level boro bead 4000 gp. To allow yourself another daily use of AA and thus another free use of a CL 18 potion.
Can the plague-bringer use their weapon infect on a bomb? I couldn't find any specifics on this, though to be fair I didn't look very thoroughly.
There is also a ridiculously cheap item for 12 gp called a bumbchucker that increases the bomb range by 10 feet. Still within point blank range, though depending on your GM this may interfere with your riding/bomb loading ability
I've never really liked firebug, as at mid/later levels you should really have no trouble hitting touch AC anyways as touch AC doesn't really scale like regular AC. Maybe look into Pragmatic activator, to make your wand versatility really vast.
Your potion of Barskin looks a bit off price (in your favor) I have 1200 gp for CL 12.
You have a hybridization funnel, invest some of that gold in a bunch of Alchemical items, especially if you're planning on using full pouch. Don't just get weapons either, grab some cool utility items like weapon blanch and tunnel creeper. Holy water bombs also are great undead/outsider splash nukes too.
With a haversack, you probably could afford to splurge on the 200 gp full alchemist lab to get that extra +1 to craft alchemy. The portable lab was designed to be carried by non-magic/dimensional bags, but the full sized one should fit.
I also don't love the tanglefoot bombs because they don't lead to anything else downstream, there are other bomb discovers that count as prerequisites for much more powerful bombs.
You're also going to need some sort of default weapon, for when you eventually run out of bombs and splash weapons: perhaps a shortbow, or crossbow or even a lance of some sorts (though proficiency might prove difficult to obtain). I think if your ride check is high enough you should be able to easily pass checks that allow you to move on your mount while reloading a cross-bow, and still fire in one round.
Also consider Improved initiative, being at the top of the order for a bomber can be amazing, catching the enemy while they are still clustered can be devastating.
The mummification discovery line is also really really neat, and might thematically fit with a crypt creeping plague slinging rodent.
I've played several alchemists *and* I've played mythic characters (including a mythic alchemist, though only to tier 3).
Gear looks good, not going to comment on that, I'd like to focus my response on mythic path/mythic feat/mythic abilities.
First off, I'll mention that our group is under the impression that the authors for mythic made the common mistake of assuming that the alchemist is an arcane spellcaster, and intended for alchemist to be able to take the Archmage path (which is the path that I ended up taking).
Our support for this assumption is due to the Archmage path features, "Remixer" (which allows you to swap around prepared extracts), Shapeshifting Mastery (which again explicitly refer to extracts), and the fact that there are mythic alchemist formula available, which you would gain with the "Mythic Spellcasting" universal path feature (even though you're not technically a spellcaster).
Although it's true that you can nab one of these Archmage options through Trickster, it wouldn't surprise me at all if the intention was for alchemists to be able to go the Archmage route.
That all out of the way, Trickster is an excellent choice, and I was very tempted to go that route myself. Most GMs should allow you to use Deadly Throw with your alchemist bombs to toss a bomb as a swift, which is extremely potent.
The Trickster Path Feature, Assured Drinker, is absolutely outstanding.
Path Dabbling should probably be used to pick up Remixer from the Archmage path, above.
All three instances of Legendary Item should be strongly considered - make your item intelligent, pay attention to the rules around intelligent items having their own actions that they can use to activate their abilities, and grab lots of instances of spellcasting.
Divine Source can be an intriguing way to pick up access to some interesting SLAs.
Mythic Spellcasting (universal path feature) and Mythic Spell Lore (mythic feat) each offer (identical) access to mythic alchemist formula, and is probably something you'll end up picking up at some point at least once.
If you end up looking at Divine Source, Legendary Item, or Mythic Spellcasting, consider pairing them with the mythic feat Mythic Paragon, which increases your mythic tier numerical value by 2 (which works exceptionally well with both Divine Source and Legendary Item.)
Strongly consider picking up Quick Draw to qualify for the mythic feat, Two-Fisted Drinker. TFD allows you to draw two potions/extracts/your mutagen as a move, and drink them both as a standard. Coupled with the mythic Trickster's Assured Drinker, this allows you to down up to three extracts as a full-round action, which is just quickened alchemist casting on steroids.
Mythic Throw Anything is another great mythic feat that shouldn't be overlooked just because it's basic - you definitely shouldn't overlook it. Getting an extra +2 to hit is nice, but tightening up your splash miss radius is great.
Drink is Life can be incredibly fun for an alchemist - even moreso if you happened to go Brewkeeper (Cayden Cailean-themed alchemist prestige class).
Honestly, though, there are so many great mythic options that you're practically assured to create something that's incredibly powerful (though I don't think I can recommend Remixer and Assured Drinker enough as your first two mythic path features).
I've played several alchemists *and* I've played mythic characters (including a mythic alchemist, though only to tier 3)....I am starting at Tier 1, Level 6, though the others in the game are tier 2, level 6-7, I should get tier 2 soon.
I had a big list of path abilities I was considering, and I am unsure what I want to do as far as mythic feats and path abilities in general. I do like Assured drinker, probably at tier 1, though I am currently at a loss for the mythic feat to add. Mythic rapid shot, Mythic throw anything, Mythic point blank shot, Mythic brew potion, The reccomended Two-fisted drinker, or taking more path abilities....
Legendary item is of course a fun choice, but I always have the issue of what spell list and spells to take, And I would need to do a LOT more looking into extracts to see what mythic ones there are, and what is worth burning a mythic on, especially since it'll only work on one ally.
If you're allowed to take Mythic Brew Potion, I absolutely would - keep in mind that an allied spellcaster can provide the spell that you brew - but be aware that it is a third party mythic feat (from Legendary Games, I think?)
Mythic Rapid Shot is great, but... I assume you're looking to pair it with fast bombs at some point? The problem I have with fast bombs is that you can burn through your daily bomb usage incredibly quickly (I played an Explosive Missile-focused grenadier for my mythic alchemist, so I went the slow, steady, one shot per round route).
Extra Path Ability is a totally legitimate Mythic feat choice, but it does have a Mythic Tier 3 prerequisite.
I honestly ended up using one of my mythic feats on just picking up a bonus regular feat; we hit tier 3 at the same time we hit level 16, and I used my mythic feat on Extra Discovery (Grand Cognatogen).
Yep, there are a couple weird things you can do with Mythic feats.
Unlike normal feats, you can elect to just save your Mythic feat and take it later.
But also directly under the description of the mythic feat feature, it states:
Mythic Feat: Select one mythic feat or non-mythic feat as a bonus feat. You must qualify for this feat normally. You gain another mythic feat at 3rd tier, and again every 2 tiers thereafter.