First off, since this is a review of a way to beat the game with any monster, I will state the stats of my final monster used to beat the game.

Monster-
Life - 376
Def- 999
Strength - 999
Accuracy - 800
Speed  - 40
Intellect - 0

General traits that are helpful
-Tough Skin
- Accuracy Up
-Damage boosting ability (eg Sharp Claw)

Justification for these traits
-With Tough skin and 999 Defense you arguably need 300 life, as this is the amount of damage 3 attacks from the phoenix will deal in damage, they did about 125 to me without Tough Skin. With Tough Skin, the boss now deals about 100 damage, which boosts you to being able to survive the three assumed hits at 301 as opposed to 375 life. With 800 accuracy your hit rate should be around 55% without any damage enhancement from other traits, and without hit rate boosting abilities. This decreases the life requirement to 300, but since this is a general guide the monster needs about 400 life to survive the additional damage received from the final boss' abilities, and removes 3 training sessions with a 999 coach.
-With Accuracy Up or any accuracy enhancing traits, it is now less difficult to defeat the final boss, and accuracy can be sacrificed down to 750 with still a 50% hit rate (assumed for this guide as you need to deliver 2 hits onto the boss. This trait only gives you 2 reduced training sessions with a 999 coach but is still relevant
-Since these are your highest stats 999, by having a 15% boost to damage from your primary ability, you are able to reduce more than 4 training sessions with a 999 coach, making this the most desirable stat by far
*Note*
-Since all monsters start with at least 1 physical damage ability I am advocating strength as opposed to intellect and speed. The reason for this is the internal strength life defense synergy, and advanced trainings can boost 2 of these at any time, whereas intellect training will normally drain either health or defense. While a 999 intellect monster is viable, it will by no means work on all monsters, nor has it been tested by me, since using this guide will almost take up the life of your monster (eg the 4.5 year hard cap for aging)

Theoretical Monster which can win
-Has All 3 traits
Life-301
Strength - 875
Defense-999
Int-0
Speed-0
Accuracy- 750

Now that this has been established lets look at the best month to breed your victory monster. By Generation from the shrine
-Generation of the monster:
The Best time to generate a monster, is the week after an official AGIMA, Class Cup. The reason for this being is rather intuitive, since their are 4 cups a year, and you need to win all of them to advance as quickly as possible to have the 1 year needed (as enforced by the game), to become a super S trainer and then fight the final boss. By giving yourself the most time to get out of the Easy (at this point), D and E cups, you also give yourself the best opportunity to have the most time for mistakes at the higher levels of breeding, and or give yourself better odds of negating bad Random Number Generation failure states, or critical fails on attempts to gain attributes from the trainer.
-Generate A monster with the most Letters Possible.
Since this guide assumes you have plentiful gold and are stuck at the S rank, what you should make sure you are always doing is creating a 9 character monster. These monsters get slight boosts to their stats that less letter creations don't, and give you higher base stats to work with on making the final push to beat Canute.

Coaching

-Make Sure you Use the best coaches possible
  Since I am assuming you have 999 coaches for all stats (Except Life and Accuracy), lower stat allotted coaches will not level up these stats as quickly and therefore will force you to make more compromises on your monsters. With a 999 Life, Defense, Strength Coach, which I did not have, you will be able to level your life even higher by sheer natural merit of the training you will be doing. Please see the Life Defense, Strength coach synergy
Make Sure you do not do the 1 month ANGIMA training. This training is often times very weak for the 4 weeks wasted, and will not generate as much stat boosting as a 999/999 coach would over that 4 week period. For example, training with the ANGIMA strength type coach only gave me 45 Life 35 defense and 40 strength. In 1 week of training in the strength/defense hybrid, I gained 30 strength 18 defense. This means it is less than optimal to train this way, as by stat cleaving (Ie strength defense, life defense, strength life, defense life), I gain all of this in 3 weeks and can use the 4th week to rest my monster, would net me the following stats 60 strength, 54 Defense, 54 Life, which is far superior than the above gains from training with the ANGIMA coach.

Items Needed
-1 of everything from the shop

Training priorities
Strength>Defense>Life (up to 400)>Accuracy (up to 700) (Before 700 in any stat)
After 700 via stat cleaving with the exception of accuracy the stats change priority and after 900 it shifts downward again. IF you hit the hard cap for a stat listed above you are good, and should not train it
A monster with 900 strength 500 defense should instead go for the defense life training or the life strength training, as the cleave still gives 17 of the secondary stat.

Time Taken For a non-Tough Skin and non optimally generated monster (generated the week before an ANGIMA tournament), 4 years 2 weeks.

Explanation of terms:
Skill cleave- the fact that training with a coach gives both a primary and secondary attribute equal to 30+ and 17+ in the two stats respectively.

TLDR can be found in the stats I used