So sentence structure is the basic format sentences should take (have you ever in grammar courses graphed a sentence?) and informs how to parse the language. Typically, in English, Sentences follow a [subject clause][verb clause][predicate clause], though imperative (ordering) sentences can have an implied "You" as the subject and no predicate. The sentence "Go!" is the shortest valid sentence in the English Language.
Of course, English being a "Borg" of languages, the format above is given weight to move around. Because English does not use gender to link adjectives and nouns to each other or their status as subject or predicate, it's not as mobile. Typically the verb must always separate the subject and predicate. But they need not be in SVP order... Yoda speak is perfectly valid, which will give a PVS that parses identically:
Luminous beings are we, not this crude matter == We are luminous beings, not this crude matter.
In both cases, the subject (We) is understood to be (Are being the second person plural of To Be) the predicate noun (luminous beings). The second part, a counter-conjunctive predicate clause. Since the Verb and Subject are the same, the clause stands alone.
Here, it's not so much the structure as it is the formatting of them for narrative flow.
First, your verbal voice is not consistent. Your two verbs are, in their infinitve state, "to climb" and "to remember" but they are "active voice" and "passive voice" respectively. Tense (past/present/future) and voice (active/passive) should remain consistent. Luckily, you already have a simple way to fix this. Try this re-write on for size:
I climbed up the arm into the cockpit. I hoped I could remember how to pilot a mech.
Now your verbs are "to climb" and "to hope" with the "remember" still in the passive voice which makes it an action you hope you can do.
But wait there's more!
In my opinion, in scenes with a high degree of dynamic actions (such as fight scenes or scenes where you're prepping for an imminant attack or other hurried movement is going on), quick simple sentences are the best. Trim as much as you can and if you need to include it, try and make it a second. In your case, you have a third.
I climbed up the arm into the cockpit. I could remember how to pilot a mech. I hoped.
Here, we break our rule for the sake of character, storybuilding, and a minor bit of comic relief. Here, your first person narrator is first describing what he was physically doing, then why he was doing it... then correcting himself in the moment, introducing a bit of doubt. Already you're setting up your audience for an interesting fight scene... this guy is confident enough to get into the pilot's seat of a Mech to fight... but as we're reminded, he hasn't done this in a while... sure he can get back behind the wheel of a Mech like getting back on a bicycle after the same amount of time away from that... but he's going into a fight... the mech equivelent of getting back on the bicycle, and then expecting to win a BMX competition. No Pressure.
The fight to come can then milk some drama or comedy with the hero making a few mistakes against his foe, before he figures the whole system out and manages an upset victory. Could be a serious moment, though the flubs could be played for some laughs (think about how in any Marvel film there's almost always a part where the hero has a fight that knocks him around and gets some humorous pratfalls that amount to a minor victory... but not one that is decisive.).