I've been stuck on Akiyos for a while now. I can get as far as defeating both the Nytekries, but then I can't seem to manage to take down Akiyos before he kills my party.

I've been using this Shadow / Air / Air team:
Shadow
- max stat
- fully ranked
- reaver's primordial equipment, where relic and armour are +4, and bracers are +3

First Air
- max stat
- fully ranked
- storm caller's primordial equipment, where relic and armour are +4, and bracers are +3

Second Air
- minor supermax stat
- all abilities are rank 4
- storm caller's primordial equipment, where relic and armour are +4, and bracers are +3

I have fully upgraded barracks except for the final trading post upgrade, but I have some superior ent flasks I got from discount bundles during events.

I've been using the following bonuses:
- rank 5 bless
- rank 5 mega bosses and bosses bonus
- superior ent flask of protection on the shadow pet
- superior ent flask of strength on each of the air pets
- exceptional grove draughts to revive pets when they die

My strategy has been:
- first focus on taking out both Nytes at the same time, doing even damage to both
- continuously taunt with shadow, and activate shadow's ability 5 early
- activate both air's ability 5s as soon as they start to lose significant health
- block with all pets when Akiyos is at full mana
- revive any dead pets immediately with exceptional grove draughts
- once both Nytes are dead, switch to attacking Akiyos directly

I'm going to try a Shadow / Light / Air team instead and see if that works any better, but any tips would be greatly appreciated in the mean time! Thanks in advance!

okay, so your strategy issue is probably pretty much in the 'focus on taking out the nytes first'- Aykios gets stronger if a bird is taken out (and vice versa.)

I'd suggest you could try our strategy, though it might need to be altered for the different team setup
> Focus on Aykios
> at something like 60-80 mana he either will or won't stick a crosshairs on either slot 2 or 3 (I swap my earth tank to 3 and hope he aims there instead of slot2 with my team, not sure how it'd work on a shadow/2air team). Whether he does or doesn't is probably based on the amount of damage done in the first round until that point. He will do the targeting every second round from the first time he does it in (so mana rounds 1, 3, 5, etc OR 2, 4, 6, etc.)
When the crosshairs are placed, the nytes will get two buff icons each. Doing enough damage to them will remove them before they time out.
Attack the Nytes while those are active (while also blocking ayk's full mana) until the buffs are gone. I'm pretty sure they get angry if you attack Ayks while they have one of the two active? Been a while since I read their tooltips.
Once the buffs are gone, you can go back to Aykios-punching.

Basically you're trying to whittle them down somewhat equally so you can take them out in relatively quick succession.
Once they're about 1/3 HP it should be fairly safe to start KO-ing with Decimates (I usually take out Aykios first personally, means I don't' have to worry about continued swapping and blocking)