None of your creatures is able to take down the Spike Cannibal by itself, so you’ll need help from the cards in your hand. To do that, however, you need more mana, and that’s where your Krosan Restorer comes in. Shambling Shell in particular can help you out twice ― once in the graveyard, and once on the battlefield for its ability.

1. During your upkeep phase, tap Living Inferno to activate its ability, targeting your Slitherhead (1 damage), your Jagged Poppet (2 damage), and Demet’s Spike Cannibal (5 damage). Slitherhead and Living Inferno both die. (You now have two cards in your graveyard: Slitherhead and Living Inferno.)
2. Jagged Poppet’s ability triggers, forcing you to discard two cards. Choose to discard Lava Dart and Shambling Shell. (You now have four cards in your graveyard: Slitherhead, Living Inferno, Lava Dart, and Shambling Shell.)
3. Declare the end of your upkeep phase, and move to your draw step.
4. When you would draw a card during your draw step, instead choose to replace the draw with Shambling Shell’s dredge 3 ability. Shambling Shell returns to your hand, and you put the top three cards of your library into your graveyard. (You now have six cards in your graveyard: Slitherhead, Living Inferno, Lava Dart, and three dredged cards.)
5. Tap one swamp to add B, one mountain to add R (used as generic mana), and Shivan Oasis to add G to your mana pool.
6. Spend 1BG to cast Shambling Shell. When Shambling Shell enters the battlefield, Death Match’s ability triggers. Choose to give Demet’s Spike Cannibal -3/-3 until end of turn. Spike Cannibal is now a 15/15 creature (with 5 damage on it).
7. Sacrifice Shambling Shell to activate its ability. Choose to put a +1/+1 counter on your Bloodshot Trainee. Bloodshot Trainee is now a 3/4 creature. (You now have seven cards in your graveyard: Slitherhead, Living Inferno, Lava Dart, three dredged cards, and Shambling Shell.)
8. Because you now have seven cards in your graveyard, you may now tap Krosan Restorer to activate its threshold ability. Choose to untap all three of your lands.
9. Spend 0 to activate Slitherhead’s Scavenge ability from your graveyard, exiling Slitherhead and putting a +1/+1 counter on Bloodshot Trainee. Bloodshot Trainee is now a 4/5 creature.
10. Because Bloodshot Trainee’s power is 4, you may now tap it to activate its ability. Choose to have Bloodshot Trainee deal 4 damage to Demet’s Spike Cannibal. Spike Cannibal now has a total of 9 damage on it.
11. Tap one swamp to add B, one mountain to add R (used as generic mana), and Shivan Oasis to add G to your mana pool.
12. Spend 1BG to cast Grim Contest, targeting your Bloodshot Trainee and Demet’s Spike Cannibal. Bloodshot Trainee deals 5 damage to Spike Cannibal, and Spike Cannibal deals 15 damage to Bloodshot Trainee. Bloodshot Trainee dies. Spike Cannibal now has a total of 14 damage on it.
13. Sacrifice a mountain to pay Lava Dart’s Flashback cost. Choose to have Lava Dart deal 1 damage to Demet’s Spike Cannibal.
14. Demet’s Spike Cannibal is now a 15/15 creature with a total of 15 damage on it, and dies.

Update (22/04/2015): Anonycat notes a far simpler solution:

1. During your upkeep phase, tap one swamp to add B (used as generic mana), one mountain to add R (used as generic mana), and Shivan Oasis to add G to your mana pool.
2. Spend 1G and sacrifice a swamp to activate Squirrel Wrangler’s first ability, putting two 1/1 Squirrel tokens onto the battlefield.
3. Demet’s Death Match triggers twice due to the Squirrel tokens. Choose to target Demet’s Spike Cannibal both times; Spike Cannibal is now a 12/12 creature.
4. Tap Krosan Restorer to untap your Shivan Oasis.
5. Tap Shivan Oasis to add G to your mana pool.
6. Spend 1G and sacrifice a mountain to activate Squirrel Wrangler’s first ability, putting two 1/1 Squirrel tokens onto the battlefield.
7. Demet’s Death Match triggers twice due to the Squirrel tokens. Choose to target Demet’s Spike Cannibal both times; Spike Cannibal is now a 6/6 creature.
8. Tap Living Inferno to activate its ability, targeting Demet’s Spike Cannibal (6 damage) and any other opportune legal target for 2 damage. Demet’s Spike Cannibal dies.