Level Up
Evo Icicle Spear
1 Icicle Spear [HS,R]
1 Curse [HS]
1 Encore [HS]
1 Astonish
1 Meditate
1 Mist
1 Ice Shard
3 Meditate [R]
8 Mist [R]
10 Ice Shard [R]
15 Spite
18 Shadow Punch
23 Mean Look
25 Avalanche
30 Ice Ball
33 Ominous Wind
38 Payback 
40 Focus Energy
45 Ice Hammer
50 Grudge
55 Phantom Force
60 Focus Punch

Level Up Numbers: Focus Punch's Prime Factors are 2, 3, 5 and 5. Hey look Level Up numbers! 3 - 5 - 2 - 5 pattern, then a string of 5s.

Ghost Dislikes You: Moves like Spite, Grudge, and Mean Look should give you a hint as to how Skadi feels about your continued existence. Also comes with sarcastic clapping (Encore!)

Meditation: Focus Punch, Focus Energy, Medidate provides the idea of something that is able to clear it's mind and so on, helping justify Focus Punch.

Eggs - Dragon
Double Slap [Salandit]
Haze [Arbok]
Ice Fang [Arbok]
Tail Whip [Dragalge]
Wrap [Arbok]

Dragon because Snake-like thingy. Mostly Snakey moves, with more Ice Flavour.

TMs:
TM02: Dragon Claw
TM04: Calm Mind
TM06: Toxic
TM07: Hail
TM10: Hidden Power
TM12: Taunt
TM13: Ice Beam
TM14: Blizzard
TM15: Hyper Beam
TM17: Protect
TM18: Rain Dance
TM21: Frustration
TM27: Return
TM29: Psychic
TM30: Shadow Ball
TM32: Double Team
TM41: Torment
TM42: Facade
TM44: Rest
TM45: Attract
TM46: Thief
TM48: Round
TM52: Focus Blast
TM54: False Swipe
TM56: Fling
TM59: Brutal Swing
TM64: Explosion
TM65: Shadow Claw
TM66: Payback
TM68: Giga Impact
TM77: Psych Up
TM79: Frost Breath
TM87: Swagger
TM88: Sleep Talk
TM90: Substitute
TM97: Dark Pulse
TM100: Confide

Tutors:
Bind
Endeavor
Focus Punch
Helping Hand
Ice Punch
Icy Wind
Iron Tail
Laser Focus
Snatch
Snore
Spite
Throat Chop
Uproar