Shinzou o Sasageyo!

All-of-sacrifice as-for, now this time-of-sake-for, let's-offer

捧げる ('to offer / dedicate / consecrate') is the verb for offering at a shrine or before a god — distinct from plain あげる. The volitional 捧げよう is the song's signature: 'let's offer (it).' Combines a ritual register with the urgency of battle.

Let's-offer let's-offer heart (obj) let's-offer

心臓 (shinzou) is the heart-as-organ — the literal beating muscle, distinct from the metaphysical 心 (kokoro). The Survey Corps salute (right fist over the heart) is the choreography behind the line — soldiers giving their physical hearts, not their abstract devotion.

All-of-effort as-for, now this time-of-sake-for, sing-should victory (obj), with-that seize-imp.

〜べき ('should / ought to V') attaches to verb-dictionary form. 歌うべき勝利 ('victory that should be sung [about]') = 'a victory worth chronicling.' 掴み取る ('grasp-and-take') is a compound verb — its imperative 掴み取れ commands the seizure.

Monster (subj), person-with-resembled face (obj) is-doing-contempt

化け物 ('changing-thing' = monster, especially shape-shifter) is the right word for AOT's Titans, who are humans-turned-monsters. してやがる is the contemptuous version of している ('is doing') — adds the speaker's spite. Used for things enemies do that disgust the speaker.

This world-from one-animal not-remaining, them (obj) exterminate-do-for-them

一匹 uses 匹 (the counter for small animals or insects) — calling Titans 一匹 dehumanizes them, treats them as vermin. 残らず ('without remaining' = without exception) intensifies the enumeration. 〜てやる is rough masculine determination — the giving direction is downward (to enemies, with disdain). The line is Eren's defining vow.

First-at started-saying thing-as-for, who? such-thing don't-even-remember but

言い出す ('start saying' = first say / bring up) — used to attribute the originating utterance. 覚えちゃいない is casual contraction of 覚えてはいない — same construction as 諦めちゃいない from 'Redo.' Rough masculine register: 'I haven't remembered.'

Cannot-forget anger (subj) exists, without-fail exterminate-do-for-them

怒り (ikari, 'anger / rage') is the formal word — distinct from 怒り狂う ('rage') or イライラ ('annoyance'). 必ず ('without fail / certainly') intensifies the vow. The repetition of 駆逐してやる as a refrain is the song's defining murderous-resolve beat.

Unknown-of-beyond as-for, what-kind-of place-to is-connected

未知の先 ('beyond the unknown') is the world the Survey Corps fights to reach. 繋がる ('to be connected') is the verb for paths leading somewhere — implies 'where does it open onto?' The question with 〜ている is contemplative, not interrogative.

Just offered life (obj) sustenance-as, blooms

〜を糧に ('as one's sustenance / nourished by ~') is the literary 'use X as fuel.' 糧 (kate) is the formal/literary 'food' — sustenance, provender. The structure says: dead lives feed the bloom of what comes next.

Promise-of-land as-for, paradise-of-edge

約束の地 ('the promised land') is the Biblical phrase translated word-for-word — 約束 ('promise') + の地 ('land'). Common in J-RPG / fantasy as the destination beyond hardship.

That day humanity as-for, remembered, sky-by being-ruled-was terror (obj)

Direct callback to AOT's pilot episode opening narration: 'On that day, humanity remembered…' (あの日人類は思い出した). The line is the show's signature line — placing it in the song collapses the song into fan service for viewers who recognize it instantly.

Birdcage-of-inside-in being-captive-was humiliation (obj)

鳥籠 ('birdcage') is AOT's metaphor for the walls of Paradis — humans living inside a cage they thought was a refuge. 屈辱 (kutsujoku) is formal 'humiliation' — used for collective historical shame, not personal embarrassment.

Dusk-at draw-bow wings (obj) shoulder, that trajectory (subj) freedom-toward-road becomes

翼 (tsubasa, 'wings') refers to the Wings of Freedom — the Survey Corps emblem (a pair of crossed wings, blue and white). 黄昏に弓引く ('drawing bows at dusk') is mythological imagery — the army at the threshold between day and night. 軌跡 ('trajectory / locus') is the path traced by movement — same noun as in the Frieren song.

All-of-hardship as-for, this time-of-sake-for, fleeting-classical life (obj) burning meaning-into transforming

儚き ('fleeting / ephemeral' in literary attributive) — modern equivalent: 儚い. 命を意味に変える ('change life into meaning') is the song's distillation of sacrifice — the dead become reasons. The hymn-like register is intentional: this is a march, not a confession.

Be-proud-should miracle (obj) that body-with draw-out-imp.

誇るべき (literally 'should-be-proud-of') is the second 〜べき of the song — pairs with 歌うべき勝利 from the chorus. その身で ('with that body') uses 身 (mi, 'body / one's person') — more elevated than 体 (karada). 描き出す ('draw-out / depict-completely') in imperative ends the song with a command to manifest the miracle physically.