Walking Ballista has at least two +1/+1 counters on it.

Activate Heliod by paying , giving Walking Ballista lifelink until end of turn.
Activate Walking Ballista's second ability by removing a +1/+1 counter, dealing 1 damage to any target.
Walking Ballista's lifelink triggers, causing you to gain 1 life.
Heliod triggers, putting a +1/+! counter on Walking Ballista.
Repeat from step 2.

Walking Ballista on the battlefield with a +1/+1 counter on it.

Activate Walking Ballista's last ability by removing a +1/+1 counter from it, dealing 1 damage to itself.
Walking Ballista dies, triggering its undying ability, returning it from your graveyard to the battlefield with a +1/+1 counter on it.
Repeat.

Walking Ballista has at least two +1/+1 counters on it.
You have a way to give Walking Ballista lifelink.

Give Walking Ballista lifelink.
Activate Walking Ballista's second ability by removing a +1/+1 counter from it, dealing 1 damage to any target and causing you to gain 1 life.
Archangel of Thune triggers, putting a +1/+1 counter on each creature you control.
Repeat from step 2.

Activate Urza's first ability by tapping Sword of the Meek, adding .
Activate Thopter Foundry by paying and sacrificing Sword of the Meek, creating a 1/1 Thopter creature token with flying and causing you to gain 1 life.
The Thopter enters the battlefield, triggering Sword of the Meek, causing you to return Sword of the Meek from your graveyard to the battlefield attached to the Thopter.
Repeat.
Once you have an infinite amount of Thopter tokens, you may tap them using Urza's first ability to get infinite , and then use the mana to activate Urza's second ability infinite times.

Use Mindslaver's ability targeting an opponent.
Activate Academy Ruins's ability targeting Mindslaver in graveyard.
Pass to opponent's turn.
Pass to your turn and draw Mindslaver.
Play Mindslaver, use it, and target it with Academy Ruins.

Emry does not have summoning sickness.

Activate Mindslaver by paying , tapping and sacrificing it, gaining control of target player's next turn.
Activate Emry by tapping it, allowing you to cast Mindslaver from your graveyard this turn.
Cast Mindslaver from your graveyard by paying .
Pass the turn.
End the controlled opponent turn.
Repeat.

Cast Rite of Replication with kicker by paying , creating five token copies of Terror of the Peaks.
The five Terror of the Peaks tokens enter the battlefield, triggering the nontoken Terror of the Peaks five times and each Terror of the Peaks token four times.
Resolve all Terror of the Peaks triggers, dealing 125 damage divided among a maximum of 25 targets.

Play Vesuva, and choose to have it enter the battlefield as a copy of Titania.
Put Vesuva into your graveyard due to the legend rule.
Vesuva's first ability and second ability trigger, as well as Titania's second ability.
Resolve the second Vesuva trigger and the Titania trigger, creating two 5/3 Elemental creature tokens.
Resolve the first Vesuva trigger, returning it from your graveyard to the battlefield as a copy of Titania.
Repeat from step 2.

You control at least five enchantments.

Activate Parallax Wave by removing a fade counter from it, targeting any creature an opponent controls.
You may repeat step 1 as desired until Parallax Wave has exactly one fade counter on it.
Activate Parallax Wave by removing a fade counter from it, exiling itself.
When Parallax Wave leaves the battlefield, it triggers, returning all cards exiled with it to the battlefield under their owner's control.
Resolve all Parallax Wave abilities from steps 1 and 2, exiling the chosen creatures.
Repeat as desired, or whenever a creature enters the battlefield under an opponent's control.
You may use this method to blink creatures/enchantments you control if you resolve the Parallax Wave abilities before exiling Parallax Wave.

Murderous Redcap does not have any -1/-1 counters.

Activate Altar of Dementia by sacrificing Murderous Redcap.
Murderous Redcap's persist ability triggers, returning itself to the battlefield.
Anafenza and Murderous Redcap trigger.
Resolve the Anafenza trigger, putting a +1/+1 counter on Murderous Redcap.
Resolve the Murderous Redcap trigger, dealing damage equal to its power to any target.
Resolve the Altar of Dementia ability, causing target player to mill two cards.
Repeat.

Cast Murderous Redcap by paying , which enters with a +1/+1 counter on it due to Renata.
When Murderous Redcap enters the battlefield, it triggers, dealing an amount of damage to itself equal to its power.
Murderous Redcap dies as a state-based action due to having 0 toughness.
Murderous Redcap's persist ability triggers, returning it from your graveyard to the battlefield without a -1/-1 counter on it due to Renata.
Repeat from step 2.

Kitchen Finks does not have a -1/-1 counter on it.

Activate Altar of Dementia by sacrificing Kitchen Finks.
Kitchen Finks dies, triggering its persist ability, returning Kitchen Finks from your graveyard to the battlefield with a -1/-1 counter on it.
Kitchen Finks enters the battlefield, causing you to gain two life.
Heliod triggers, putting a +1/+1 counter on Kitchen Finks.
Resolve the Altar of Dementia ability from step 1, causing target player to mill cards equal to Kitchen Finks' power.
Repeat.

Bloodspore Thrinax has a +1/+1 counter on it.

Cast Murderous Redcap by paying , which enters with a +1/+1 counter on it due to Bloodspore Thrinax.
When Murderous Redcap enters the battlefield, it triggers, dealing an amount of damage to itself equal to its power.
Murderous Redcap dies as a state-based action due to having 0 toughness.
Murderous Redcap's persist ability triggers, returning it from your graveyard to the battlefield without a -1/-1 counter on it due to Bloodspore Thrinax.
Repeat from step 2.

You control at least one additional creature with at least one +1/+1 counter.

Activate Carrion Feeder by sacrificing a creature with at least one +1/+1 counter, Carrion Feeder gets +1/+1 until end of turn.
Basri's Lieutenant trigger, creating a 2/2 Knight token.
When Knight token enters the battlefield, Renata trigger, putting a +1/+1 counter on Knight token.
Resolve the Goblin Bombardment ability by dealing 1 damage to any target.
Repeat.

You control at least one additional creature with at least one +1/+1 counter.

Activate Altar of Dementia by sacrificing a creature with at least one +1/+1 counter.
Basri's Lieutenant trigger, creating a 2/2 Knight token.
When Knight token enters the battlefield, Renata trigger, putting a +1/+1 counter on Knight token.
Resolve the Altar of Dementia ability, causing target player to mill cards equal to the sacrificed creature's power.
Repeat.

Bloodspore Thrinax has at least one +1/+1 counter on it.
You control at least one additional creature that has a +1/+1 counter on it.

Activate Altar of Dementia by sacrificing another creature with a +1/+1 counter on it.
When the creature dies, Basri's Lieutenant's second ability triggers, creating a 2/2 Knight creature token that enters the battlefield with at least one +1/+1 counter due to Bloodspore Thrinax.
Resolve the Altar of Dementia ability, causing target player to mill cards equal to the sacrificed creature's power.
Repeat.

You control at least two other Golems.

Cast Rite of Replication with kicker by paying , targeting Precursor Golem.
Precursor Golem triggers, creating a kicked copy of Rite of Replication targeting every other Golem.
Resolve the first Rite of Replication, creating five token copies of the Golem it is targeting.
If the Golem was Percursor Golem, the Percursor Golem tokens enter the battlefield, creating a total of ten 3/3 Golem artifact creature tokens.
Repeat from step 3 for each other Rite of Replication.
Cast Slip Through Space by paying , targeting any Golem.
The six Percursor Golems each trigger.
Resolve the first Percursor Golem trigger, creating a copy of Slip Through Space targeting every other Golem.
Repeat step 8 for each remaining trigger.
Resolve the first Slip Through Space, causing you to draw a card.
Repeat step 10 until you draw from an empty library, causing you to win the game.

Cast Emrakul for .
Emrakul triggers, granting you an extra turn after this one.
Tap Karakas to return Emrakul to your hand.