Name of the Eternal Pokémon: Gabite-Eternal
New Type: Dragon / Steel
New Stat distribution: 83 (+15) / 101 (+11) / 75 (+10) / 110 (+60) / 85 (+30) / 145 (+63)
Signature Move: Gem Seeker - Steel, Special, 110 BP, 5 PP, 85% Acc | Ignores accuracy checks against Rock-types
Design/Flavor: Its knack for shiny objects has driven it to the point of searching tirelessly for years on end. Over the course of its search, its scales ended up covered in iridescent dust that gives off a radiant white color when exposed to light. It is known for its enhanced speed and its ability to release intense mental energy with all things rocky on the forefront of its mind.
Competitive Analysis: Fast mixed attacker with good typing. Can go physical with Swords Dance or make use of its high-powered special attacking options.
Name of the Eternal Pokémon: Zweilous-Eternal
New Stat distribution: 99 (+27) / 115 (+30) / 109 (+39) / 109 (+44) / 94 (+24) / 73 (+15)
Signature Move: Dubious Dusk - Dark, Physical, ??? BP, 10 PP | Hits 2 times; each hit is randomly decided to have 30 BP, 40 BP, 50 BP, or 60 BP; ignores accuracy checks
Design/Flavor: The two heads are horribly uncoordinated, but they do agree on one thing: that the best way to prove oneself is by hauling out the big guns and attacking with all their might. Sometimes, however, they may have different perceptions of what "all their might" is. Regardless, they have reluctantly formed a lasting bond (being physically attached to each other, but not so much emotionally) and honed themselves with the battles that they've fought.
Competitive Analysis: Weird typing for a tank. Has spammable Dark STAB, not-so-spammable Dragon STAB, and perchance Earth Power and/or Head Smash for coverage.
Name of the Eternal Pokémon: Sliggoo-Eternal
New Stat distribution: 87 (+19) / 84 (+9) / 123 (+70) / 84 (+1) / 118 (+5) / 103 (+43)
Signature Move: Slimy Slip - Dragon, Physical, 75 BP, 15 PP, 100% Acc | Removes the target's held item and allows the user to switch out; makes contact
Design/Flavor: Less viscous than its mortal counterpart, yet somehow tougher to take down. This Sliggoo has changed over time to where it can slither around nimbly and spotlessly, regardless what it does—be it scavenging for food, gliding across a body of water, or even meeting the sole of a human's shoe.
Competitive Analysis: Item removal and pivoting, something that no one of the ordinary Sliggoo family can do, compressed into one moveslot. Problem is it can't do much else with its low offenses and otherwise barren utility movepool.
Name of the Eternal Pokémon: Hakamo-o-Eternal
New Type: Fighting / Flying
New Stat distribution: 94 (+39) / 115 (+40) / 95 (+5) / 95 (+30) / 85 (+15) / 115 (+50)
Signature Move: Scale Shift - Flying, Other, 20 PP | The user makes its scales more aerodynamic, raising its Speed by 1 stage and doubling its Flying-type power on the next turn. | Z-Move effect: +1 Speed
Design/Flavor: Eternal Hakamo-o has its leaping technique taken to the next level. Through honing of this technique and frequently testing its mettle against avian species, it has become nimble enough and experienced enough to be perceived behavior-wise as avian. However, its predatory nature and fighting techniques remain intact.
Competitive Analysis: Its signature move gives Aerial Ace some merit, and its dual STABs complement each other well despite being weak. Having Earthquake, Rock Slide, and Shadow Claw for coverage helps, though. Not to mention it has swell physically offensive prowess. Hmm...and perhaps Focus Blast off base 95 Special Attack isn't too bad...
9/8 EDIT: All right, that takes care of all my submissions.