Use the lower level monsters and keep destroying keith's monsters. Don't attack if he has a face-down trap since it could be rare-metalmoprh. Set a magnetic mosquito if you think he will tribute summon either blowback or barrel dragon. Use acid raid if you don't have mosquito to destroy his tribute monsters. It's best to summon BEUD during second to last turn to avoid it getting destroyed early. On the last turn, summon vassal and use the union attack combo.
Summon either the hunter or jerry and destroy keith's monsters when they are in defense position to not lower his LP. If they are summoned in attack position, switch it to defense using otohime on the next turn. Acid raid if their attack is higher than yours, or mirror wall to defend as well as reducing your LP. Lower your LP to more than half of keith's LP and keep destroying his monsters so the BEUD can get a direct attack to deal 10,000 damage after equipped with sword of deep-seated.
Since the ATK of Twin-Barrel Dragon is 1700 and same to that of Axe Raider, the highest ATK level 4 monster you can get, you need to use equips spells or other ATK boost cards to get your monsters to defeat the dragon.
Use Spell/Trap removals
Destroying Keith's Machine Conversion Factory, Second Coin Toss, and Rare Metalmorph is important to help your monsters to beat Keith's Machine monsters.
I use this Breeding Jam Machine to farm Keith lvl 40. The goal is to give BJM to Keith in your first turn, either by using exchange gift or Surprise Present skill, and to summon UG or Rai. This is a quite cheap deck to farm Keith with almost 100% win ratio and 8k score.
If you don't have surprise present skill, you can try a version using Restart skill and some reload/magial mallet to ensure both UG/rai and GE in your first turn. However, the wining ratio of this version is barely 80 % (you can also use this version to obtain 3DS cancer for Paradox Brothers).