Curious how people build budget Gwendoyln?

Well personally I would not build any unit that don't have the best IV so I usually wait until i get a better IV and by then I would have Enough to make atleast a +5. but since you really wanna build her here are some Builds(Not the best build since I Don't have a built gwendolyn)

You can go with Marbels' Build of gwendolyn( just search Marbels Gwendolyn if you want to know)
or go for a cheap build:
Slaying lance+(this is the most amount of commitment IMO in this build)
Bonfire
Fury
Wary fighter or vantage
C skill is flexible
and CD/DD, +atk/def/res seal

For budget f2p-friendly Gwendolyn, I'd recommend something like this:

Weapon: Killer Lance / Heavy Spear (arena assault)
Special: Ignis
A: Fortress Def / Earth Boost / ATK3+ / DEF3+
B: QR / Wary Fighter (use Bonfire for this) / Sword or Lancebreaker
C: Up to preference; Threaten Atk or Ward Armor or Hone Armor

Unfortunately, Gwendolyn's potential is largely limited without DC, but even then there are so many better candidates for the skills. Hence, her best bet to stand out as a unit is to build her as a defensive tank like Lukas with a much better magical bulk but weaker offensive stats.

Ideally, you'd want to upgrade her to 5* to unlock her Killer/Slaying Lance+, but these sets you're primarily aiming to soak as much physical dmg as possible while dishing out huge bursts with Ignis every few engages while using the Killer weapon passive to proc them as often as possible. Effie is generally a better Gwendolyn in terms of offensive pressure, so you need to run her as a defensive unit to distinguish her niche.

Heavy/Slaying Spear+ are purely for those in high arena tiers where you'll be facing armor units 90% of the time, hence the effective bonus effect becomes highly valuable over on that side.

Well she can work on a budget, but you will still need to 5* her, because Killer Lance just doesnt cut it imho. Give her Fury or Fortress Def, Bonfire or Ignis, Quick Riposte/Vantage/Guard/Wary Fighter and C-Slot of choice (Armor March, Ward/Goad Armor, Fortify/Hone Armor or another Drive/Spur/Hone/Threaten)

Curious as to who I am?
You're better of not knowing.
Perhaps....even asking.
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Give Gwendolyn Renewal and Reciprocal aid so you got a nice tank healer. Bonfire or Ignis and Ward Armor for Armor parties.

I feel your sadness in the Nuzlocke
Was it a stupid death like aftermath ability or was it foreseeable?

Since Gwendolyn summons as a 3* 4* unit, I think she is one of the best characters to make a 4* merged build out of

I use a +Attack -Speed
Brave Lance
Bonfire
Death Blow
Wary Fighter
Armored Boots build

The Support Skill and C Skill can be whatever you need at the time