Legendary Ike

Weapon: Slaying Edge+ (+Spd or +Atk) / Ragnell / Wo Dao+ (+Spd)

Assist: Positional Assist

Special: Radiant Aether II

Passive A: Atk/Spd Solo / Warding Breath / Darting Breath / Kestrel Stance 3 / Distant Counter / Atk/Spd Push 4 / Atk/Res versions of all aforementioned skills

Passive B: Special Spiral

Passive C: Joint Drive Atk / Joint Drive Res / Def Smoke

Sacred Seal: Atk/Spd Solo / Quick Riposte / Atk/Def Solo / Mirror Stance

• Special Spiral is an ideal dancing partner to Radiant Aether II; after every round of combat where Radiant Aether successfully fires, Special Spiral will prepare it at a lower cooldown value (by -2) in time for Ike's next counterattack. Because Radiant Aether II already reduces its own cooldown on Turn 1 and provides both healing and great burst damage, Ike will have little problem getting it up and running while maintaining relatively good matchups against most except one-hit mages and Guard effect skills.
• Ike's weapon and A slot choices depend on your preferred level of investment and whether you want to maintain the ability to counterattacked ranged enemies. Generally speaking, there are a few flavors to this build: 
  • Slaying Edge + Atk/Spd A-slot skill: While Ike loses on distant countering properties, he would instead opt for generally better melee performance with a refined Slaying Edge and an Atk/Spd-boosted A slot of choice. The -1 CD from Slaying Edge also allows Ike to be completely independent of Breath effects. 
  • Ragnell + Breath Skill: Ike's native Ragnell grants no other effects other than granting the ability to counterattack ranged units, which is generally fair enough if you exercise discretion against powerful magic units. Some form of Breath, whether it be through running an A-slot (such as his also-native Warding Breath — preferably Ike wants Fierce or Darting Breath instead if you can help it) or running ally-provided sources (mainly, Brave Lucina's Geirskogul), is required in order to activate Radiant Aether instantly on all counterattacks since it will be left at 2 CD. 
  • Slaying Edge + Distant Counter: Maintains Ike's ability to run Distant Counter while enabling him to activate Radiant Aether II without the help of a Breath effect thanks to Slaying Edge's permanent -1 CD reduction. His ability to tank high-powered magical hits is still suspect, however. 
  • Wo Dao + Breath Skill: Wo Dao directly increases the amount of retaliation damage done by Radiant Aether, giving generally more room for one-shots as well as better healing. Like Ragnell, it requires Breath in some form to instantly activate Radiant Aether. 
• In the C slot, Ike's base Joint Drive Res is a fine budget choice as-is as it slightly improves his exploitable magic bulk. To further increase the power of Ike's counterattacks, though, Def Smoke or Joint Drive Atk would be preferred. 
• Finally, Ike will opt for Sacred Seals that improve his damage and/or follow-ups. Atk/Spd Solo is a direct solution to this, but Mirror Stance or Atk/Def Solo can be taken alternatively to raise his defenses instead. For a guaranteed follow-up regardless of Ike's Speed, Quick Riposte is also optimal and stays consistently active thanks to Radiant Aether's healing.

Weapon: Slaying Edge+ (+Def) / Carrot Cudgel+ (+Def) / Armorsmasher+ / +Spd refined versions of mentioned weapons

Assist: Positional Assist

Special: Radiant Aether II / Bonfire

Passive A: Atk/Spd Solo / Atk/Def Solo / Fury / Breath Skills / Push or Bond versions of mentioned skills

Passive B: Lull Atk/Def / Null Follow-Up / Quick Riposte / Lull Atk/Spd / Lull Spd/Def

Passive C: Joint Drive Res / Atk Smoke / Joint Drive Spd / Joint Drive Atk

Sacred Seal: Atk/Def Solo / Atk/Spd Solo / Stance or Bond versions of mentioned skills

• Yeah, let's not mince words, Ike needs stats and he's not exactly getting much of that with his base kit alone. Though it takes a considerable amount of inheritance, this build helps make use of Ike's decent attacking stats, especially his Attack, Speed, and Defense, repurposing him into a more melee-oriented unit. 
• As with the previous build, forgoing Ragnell is a mostly beneficial sacrifice despite losing out on innate Distant Counter, especially as Ike's matchups against tomes and some powerful physical ranged units can be questionable. In place of it, there a few great inheritable swords he can run:
  • Slaying Edge is yet again a great weapon to consider as it permanently reduces the cooldown of some longer-going Specials. Radiant Aether II will tend to activate at a more consistent rate of 3 CD, for example, while Bonfire takes only two actions to fire off. 
  • Carrot Cudgel is fortunately easily acquirable from Heroic Grails and grants a nice, beefy Atk/Def bonus of +5 whenever Ike is parked near his allies. The debuff immunity is also helpful against enemies attempting to brute force with Attack or Defense penalties.
  • For Arena or Arena Assault, Armorsmasher is more practical than other choices due to the majority of high-scoring teams using armored units to score high. This also makes Ike a very good check to several high-pressure armored threats such as Brave Edelgard. 
• The rest of the build is basically a mix-and-match depending on which stats / gameplay aspect you'd like to focus on.
  • The best way to fortify Ike's stats is through running double Solo skills in both his A slot and Sacred Seal. This can include Atk/Spd Solo to fix up his otherwise forgettable Speed and help him make follow-ups while avoiding those from the enemy. Atk/Def Solo is his next best bet for fortifying his physical tankiness. Push or Bond versions of these skills are also viable but have differing conditions. 
  • A Breath skill is still viable when taken with Slaying Edge and Bonfire, allowing Ike to retaliate instantly with Bonfire against initiating enemies. His default Warding Breath suits this purpose just fine without laying it hard on inheritance costs.
  • A Lull skill of choice allows Ike to skew stat comparisons in his favor more by inflicting -3 to the skill's respective stats while canceling any bonuses present on the opponent. Null Follow-Up allows Ike to safety handle units with artificial follow up manipulation skills — it pairs especially well with Armorsmasher as it disables the Fighter skill line they rely on. Finally, on a budget, just good old Quick Riposte does well, saving Ike from having to use it in the Sacred Seal and acting as his main follow-up method on Atk/Def-focused builds.

Weapon: Ragnell

Assist: Positional Assist

Special: Radiant Aether II 

Passive A: Warding Breath

Passive B: Quick Riposte

Passive C: Joint Drive Res

Sacred Seal: Atk/Def Solo / Mirror Stance / Atk/Spd Solo / Fierce Stance

• If you really don't want to treat Ike a bit luxuriously from the get-go, that's fine and dandy! As long as you replace his pretty bad default B slot (Seal Atk/Def) with the much more useful Quick Riposte — which guarantees Ike can counterattack twice as long as he's above 70% HP — he's already quite built with a somewhat antiquated but synergistic enemy phase build. Notably, Radiant Aether II's healing keeps Quick Riposte's threshold going as long as you exercise reasonable matchups. The game plan is mostly similar to the first build with just as simple finesse: End Turn and watch the Special sparks fly.
• Fortunately, the list of Seals Ike can use has gotten significantly better as years went by. Most Atk-based Solo (which offers two beefy stats swings in non-tight maps) or Stance skills (less stat boosts but works unconditionally) will do great here. Of note is Mirror Stance, which stacks up Ike's otherwise forgettable Resistance alongside Joint Drive Res and Warding Breath.