Magic: the Gathering – The end of time

Question

Thanks to NeedAName and his latest Magic: the Gathering Challenge I actually noticed there is a magic-the-gathering tag. It was quite some time ago that I played Magic the last time, but nevertheless here is my first Magic: the Gathering puzzle:

BACKGROUND:

The usual magic rules apply here. Please be explicit in mana usage in your solution where relevant.

If you're fuzzy on a rule/interaction, here is the comprehensive rulebook and here is the mtg judge chat where you can ask rulings questions that you can't find on the web.

All permanents in the given setup below are owned by their controllers

Your solution may not assume that an opponent will cooperate with you in some way (e.g. choose no to a may ability that would be bad for you). Your solution must be able to win regardless of any potential choices made by your opponents; it must be able to beat the optimal plays from them.

PUZZLE SETUP:

Opponent

Your opponent just finished his turn, during which he imprinted Walk the Aeons into Panoptic Mirror:
→

Besides this, the opponent has the following board:
, with 2 shield counters on it, , with 3 +1/+1 counters on it.

The opponent's lands: 1 tapped Island, 2 untapped Islands, 1 tapped Forest, 2 tapped Plains.

The oppoent's hand: empty.

The opponent's graveyard: empty.

The opponent has 5 life left.

You

You untapped all your permanents and drew a card. Now you have the following cards in your hand:
, , , , , .

Besides that you have the following board:
, with 3 +1/+1 counters on it, , .

Your lands: 5 untapped Islands.

Your graveyard: empty.

You have 5 life left.

Win the game in this turn – you won't get another one.

Answer 1

Mana in my pool and shield counters on opponent's Palliation Accord are written as (M:X S:Y).

1. Activate gilded lotus to generate 3 blue mana (M:3)
2. Spend 1 blue mana to activate the spellbomb targeting plaxcaster frogling (M:2)
3. Either your opponent taps out to keep the frog in play, or the frog goes to their hand, either outcome is fine. (M:2)
4. Spend 1 blue mana to cast high tide (M:1)
5. Tap 5 islands to add 10 blue mana to your mana pool (M:11)
6. Cast toymaker (M:9)

7. Cast Voltaic Construct (M:5)
8. Equip Helm of Kaldra on toymaker (M:3)
9. Activate toymaker targeting Lotus, discard Tower of Champions, opponent gains 1 shield counter (M:2 S:3)
10. Activate Voltaic Construct targeting Gilded Lotus (M:0 S:3).

You now have a mana loop. Gilded lotus can be tapped to generate three mana, and construct can be activated to untap lotus for two mana, a net gain of 1 mana of any color and 1 shield counter for your opponent.

11. Gain 15 mana using this loop, ensuring that you have at least one of each color of mana (M:15, S: 18)
12. Cast Solarion using 5 different colors of mana ($5/5$, M:8 S:18)
13. Equip Helm of Kaldra on Solarion ($5/5$, M:6 S:18)
14. Tap Solarion for its ability ($10/10$, M:6 S:19)
15. Activate Voltaic Construct targeting Solarion ($10/10$, M:4 S:19)
16. Tap Solarion ($20/20$, M:4 S:20)
17. Voltaic Construct ($20/20$, M:2 S:20)
18. Solarion ($40/40$, M:2 S:21)
19. Voltaic Construct ($40/40$, M:0 S:21)
20. Attack with Solarion (S:22), your opponent single blocks (due to silent arbiter) $5$ damage and prevents the next $22$ damage they would take using Palliation Accord. They take $40-5-22 = 13$ damage, overkilling by $8$.