I have experimented with multiple Budget Hunter decks this season. An upgraded Dragon Hunter was playable, but not great. Fully budget Face Hunter was a little better, but still not top tier.
However, this time I hit the jackpot. Combining the Boar package from Face Hunter and Dragon package from Dragon Hunter results in this fun little hybrid deck that costs only 1320 dust and I played it from Diamond 5 to Diamond 2 with a 62% winrate during my budget climb.
Dragon Hunter core is still strong and provides ways to apply pressure while maintaining board control several turns into the game, and the Boar package adds burst damage and early big minions to the mix.
Budget Dragon Boar Hunter decklist

Deck code: AAECAR8AD6gCyQThBIgFlwj+DIqtA/muA/uvA/yvA/6vA/+wA4WxA/m6A/+6AwA=
The Boar package in the deck consists of Scavenger’s Ingenuity, which can tutor and buff your Beasts. There are two types of Beasts in the deck, Stonetusk Boars for Charge damage and Phase Stalkers for pulling out Explosive Traps.
Finally, the package culminates in Scrap Shot, which is ideally used after you have played any Phase Stalkers from hand and can buff up your Boar for more damage – often usable immediately on the same turn you play Scrap Shot!
This package is complemented by a regular Dragon package with its elusive minions and Corrosive Breaths that can contest the board through the mid-game.
Budget Dragon Boar Hunter mulligan

You mulligan for your early game: Blazing Battlemage, Dwarven Sharpshooter, Scavenger’s Ingenuity, and Phase Stalker.
In slow matchups, you can also keep Faerie Dragon for a threat that is difficult to remove.
Budget Dragon Boar Hunter upgrade path

By far the biggest upgrade you can make to the deck is to replace Eaglehorn Bows with Stormhammers. They just let you swing a lot more.
After that, you should replace Evasive Wyrms with Rotnest Drakes for an earlier pressure play.
Meati has built a similar list to this, and in the most popular version of it, there are Imprisoned Felmaws instead of Scrap Shots, but Meati himself has moved on from those. I do not consider Felmaw an upgrade over Scrap Shot at this time, and at least my sample of some tens of games puts Scrap Shot above Felmaw in performance.
Budget Dragon Boar Hunter gameplay video
Finally, here is a video of me piloting the deck. I hope it showcases the strengths and weaknesses of the deck.